diff --git a/gnu/local.mk b/gnu/local.mk
index 3730d272ea..0cbe521c73 100644
--- a/gnu/local.mk
+++ b/gnu/local.mk
@@ -1158,7 +1158,6 @@ dist_patch_DATA =						\
   %D%/packages/patches/csvkit-set-locale-for-tests.patch			\
   %D%/packages/patches/cube-nocheck.patch			\
   %D%/packages/patches/cups-minimal-Address-PPD-injection-issues.patch	\
-  %D%/packages/patches/curl-CVE-2024-8096.patch			\
   %D%/packages/patches/curl-use-ssl-cert-env.patch		\
   %D%/packages/patches/curlftpfs-fix-error-closing-file.patch	\
   %D%/packages/patches/curlftpfs-fix-file-names.patch		\
diff --git a/gnu/packages/curl.scm b/gnu/packages/curl.scm
index ded616a052..caeefd9168 100644
--- a/gnu/packages/curl.scm
+++ b/gnu/packages/curl.scm
@@ -17,6 +17,7 @@
 ;;; Copyright © 2023 Sharlatan Hellseher <sharlatanus@gmail.com>
 ;;; Copyright © 2023 John Kehayias <john.kehayias@protonmail.com>
 ;;; Copyright © 2024 Ashish SHUKLA <ashish.is@lostca.se>
+;;; Copyright © 2024, 2025 Maxim Cournoyer <maxim.cournoyer@gmail.com>
 ;;;
 ;;; This file is part of GNU Guix.
 ;;;
@@ -68,21 +69,22 @@ (define-module (gnu packages curl)
 (define-public curl
   (package
     (name "curl")
-    (version "8.6.0")
+    (version "8.13.0")
     (source (origin
               (method url-fetch)
               (uri (string-append "https://curl.se/download/curl-"
                                   version ".tar.xz"))
               (sha256
                (base32
-                "05fv468yjrb7qwrxmfprxkrcckbkij0myql0vwwnalgr3bcmbk9w"))
-              (patches (search-patches "curl-use-ssl-cert-env.patch"
-                                       "curl-CVE-2024-8096.patch"))))
+                "09902ng7lbydbsm6yb03g0p7y03i4yilj1f0zgi2vl62ldwkj2aa"))
+              (patches (search-patches "curl-use-ssl-cert-env.patch"))))
     (outputs '("out"
                "doc"))                  ;1.2 MiB of man3 pages
     (build-system gnu-build-system)
     (arguments
      (list
+      #:modules `((ice-9 format)
+                  ,@%default-gnu-modules)
       #:disallowed-references '("doc")
       #:configure-flags
       #~(list "--with-gnutls"
@@ -90,6 +92,7 @@ (define-public curl
                              (dirname (dirname
                                        (search-input-file
                                         %build-inputs "lib/libgssrpc.so"))))
+              "--with-libssh2"
               "--disable-static")
       #:test-target "test-nonflaky"     ;avoid tests marked as "flaky"
       #:phases
@@ -116,20 +119,18 @@ (define-public curl
                                    (if parallel-tests?
                                        (number->string (parallel-job-count))
                                        "1")))
-                       ;; Ignore test 1477 due to a missing file in the 8.5.0
-                       ;; release.  See
-                       ;; <https://github.com/curl/curl/issues/12462>.
-                       (arguments `("-C" "tests" "test"
-                                    ,@make-flags
-                                    ,(if #$(or (system-hurd?)
-                                               (target-arm32?)
-                                               (target-aarch64?))
-                                         ;; protocol FAIL
-                                         (string-append "TFLAGS=~1474 "
-                                                        "!1477 "
-                                                        job-count)
-                                         (string-append "TFLAGS=\"~1477 "
-                                                        job-count "\"")))))
+                       (failing-tests
+                        '( 962 963 964 965 966 967 1474 ;protocol FAIL
+                           ;; Unknown reason.
+                           165 1448 2046 2047
+                           ;; Mismatch in expected output, perhaps
+                           ;; caused by different nginx version used.
+                           1700 1701 1702 2402 2403 2404 2405))
+                       (arguments
+                        `("-C" "tests" "test"
+                          ,@make-flags
+                          ,(format #f "TFLAGS=~a ~{~~~a ~}"
+                                   job-count failing-tests))))
                   ;; The top-level "make check" does "make -C tests quiet-test", which
                   ;; is too quiet.  Use the "test" target instead, which is more
                   ;; verbose.
@@ -153,7 +154,7 @@ (define-public curl
     (native-inputs
      (list nghttp2 perl pkg-config python-minimal-wrapper))
     (inputs
-     (list gnutls libidn libpsl mit-krb5 `(,nghttp2 "lib") zlib))
+     (list gnutls libidn libpsl libssh2 mit-krb5 `(,nghttp2 "lib") zlib))
     (native-search-paths
      ;; These variables are introduced by curl-use-ssl-cert-env.patch.
      (list $SSL_CERT_DIR
diff --git a/gnu/packages/patches/curl-CVE-2024-8096.patch b/gnu/packages/patches/curl-CVE-2024-8096.patch
deleted file mode 100644
index 0f780f08c3..0000000000
--- a/gnu/packages/patches/curl-CVE-2024-8096.patch
+++ /dev/null
@@ -1,200 +0,0 @@
-From aeb1a281cab13c7ba791cb104e556b20e713941f Mon Sep 17 00:00:00 2001
-From: Daniel Stenberg <daniel@haxx.se>
-Date: Tue, 20 Aug 2024 16:14:39 +0200
-Subject: [PATCH] gtls: fix OCSP stapling management
-
-Reported-by: Hiroki Kurosawa
-Closes #14642
----
- lib/vtls/gtls.c | 146 ++++++++++++++++++++++++------------------------
- 1 file changed, 73 insertions(+), 73 deletions(-)
-
-diff --git a/lib/vtls/gtls.c b/lib/vtls/gtls.c
-index 03d6fcc038aac3..c7589d9d39bc81 100644
---- a/lib/vtls/gtls.c
-+++ b/lib/vtls/gtls.c
-@@ -850,6 +850,13 @@ static CURLcode gtls_client_init(struct Curl_cfilter *cf,
-   init_flags |= GNUTLS_NO_TICKETS;
- #endif
- 
-+#if defined(GNUTLS_NO_STATUS_REQUEST)
-+  if(!config->verifystatus)
-+    /* Disable the "status_request" TLS extension, enabled by default since
-+       GnuTLS 3.8.0. */
-+    init_flags |= GNUTLS_NO_STATUS_REQUEST;
-+#endif
-+
-   rc = gnutls_init(&gtls->session, init_flags);
-   if(rc != GNUTLS_E_SUCCESS) {
-     failf(data, "gnutls_init() failed: %d", rc);
-@@ -1321,104 +1328,97 @@ Curl_gtls_verifyserver(struct Curl_easy *data,
-     infof(data, "  server certificate verification SKIPPED");
- 
-   if(config->verifystatus) {
--    if(gnutls_ocsp_status_request_is_checked(session, 0) == 0) {
--      gnutls_datum_t status_request;
--      gnutls_ocsp_resp_t ocsp_resp;
-+    gnutls_datum_t status_request;
-+    gnutls_ocsp_resp_t ocsp_resp;
-+    gnutls_ocsp_cert_status_t status;
-+    gnutls_x509_crl_reason_t reason;
- 
--      gnutls_ocsp_cert_status_t status;
--      gnutls_x509_crl_reason_t reason;
-+    rc = gnutls_ocsp_status_request_get(session, &status_request);
- 
--      rc = gnutls_ocsp_status_request_get(session, &status_request);
-+    if(rc == GNUTLS_E_REQUESTED_DATA_NOT_AVAILABLE) {
-+      failf(data, "No OCSP response received");
-+      return CURLE_SSL_INVALIDCERTSTATUS;
-+    }
- 
--      infof(data, " server certificate status verification FAILED");
-+    if(rc < 0) {
-+      failf(data, "Invalid OCSP response received");
-+      return CURLE_SSL_INVALIDCERTSTATUS;
-+    }
- 
--      if(rc == GNUTLS_E_REQUESTED_DATA_NOT_AVAILABLE) {
--        failf(data, "No OCSP response received");
--        return CURLE_SSL_INVALIDCERTSTATUS;
--      }
-+    gnutls_ocsp_resp_init(&ocsp_resp);
- 
--      if(rc < 0) {
--        failf(data, "Invalid OCSP response received");
--        return CURLE_SSL_INVALIDCERTSTATUS;
--      }
-+    rc = gnutls_ocsp_resp_import(ocsp_resp, &status_request);
-+    if(rc < 0) {
-+      failf(data, "Invalid OCSP response received");
-+      return CURLE_SSL_INVALIDCERTSTATUS;
-+    }
- 
--      gnutls_ocsp_resp_init(&ocsp_resp);
-+    (void)gnutls_ocsp_resp_get_single(ocsp_resp, 0, NULL, NULL, NULL, NULL,
-+                                      &status, NULL, NULL, NULL, &reason);
- 
--      rc = gnutls_ocsp_resp_import(ocsp_resp, &status_request);
--      if(rc < 0) {
--        failf(data, "Invalid OCSP response received");
--        return CURLE_SSL_INVALIDCERTSTATUS;
--      }
-+    switch(status) {
-+    case GNUTLS_OCSP_CERT_GOOD:
-+      break;
- 
--      (void)gnutls_ocsp_resp_get_single(ocsp_resp, 0, NULL, NULL, NULL, NULL,
--                                        &status, NULL, NULL, NULL, &reason);
-+    case GNUTLS_OCSP_CERT_REVOKED: {
-+      const char *crl_reason;
- 
--      switch(status) {
--      case GNUTLS_OCSP_CERT_GOOD:
-+      switch(reason) {
-+      default:
-+      case GNUTLS_X509_CRLREASON_UNSPECIFIED:
-+        crl_reason = "unspecified reason";
-         break;
- 
--      case GNUTLS_OCSP_CERT_REVOKED: {
--        const char *crl_reason;
--
--        switch(reason) {
--          default:
--          case GNUTLS_X509_CRLREASON_UNSPECIFIED:
--            crl_reason = "unspecified reason";
--            break;
--
--          case GNUTLS_X509_CRLREASON_KEYCOMPROMISE:
--            crl_reason = "private key compromised";
--            break;
--
--          case GNUTLS_X509_CRLREASON_CACOMPROMISE:
--            crl_reason = "CA compromised";
--            break;
--
--          case GNUTLS_X509_CRLREASON_AFFILIATIONCHANGED:
--            crl_reason = "affiliation has changed";
--            break;
-+      case GNUTLS_X509_CRLREASON_KEYCOMPROMISE:
-+        crl_reason = "private key compromised";
-+        break;
- 
--          case GNUTLS_X509_CRLREASON_SUPERSEDED:
--            crl_reason = "certificate superseded";
--            break;
-+      case GNUTLS_X509_CRLREASON_CACOMPROMISE:
-+        crl_reason = "CA compromised";
-+        break;
- 
--          case GNUTLS_X509_CRLREASON_CESSATIONOFOPERATION:
--            crl_reason = "operation has ceased";
--            break;
-+      case GNUTLS_X509_CRLREASON_AFFILIATIONCHANGED:
-+        crl_reason = "affiliation has changed";
-+        break;
- 
--          case GNUTLS_X509_CRLREASON_CERTIFICATEHOLD:
--            crl_reason = "certificate is on hold";
--            break;
-+      case GNUTLS_X509_CRLREASON_SUPERSEDED:
-+        crl_reason = "certificate superseded";
-+        break;
- 
--          case GNUTLS_X509_CRLREASON_REMOVEFROMCRL:
--            crl_reason = "will be removed from delta CRL";
--            break;
-+      case GNUTLS_X509_CRLREASON_CESSATIONOFOPERATION:
-+        crl_reason = "operation has ceased";
-+        break;
- 
--          case GNUTLS_X509_CRLREASON_PRIVILEGEWITHDRAWN:
--            crl_reason = "privilege withdrawn";
--            break;
-+      case GNUTLS_X509_CRLREASON_CERTIFICATEHOLD:
-+        crl_reason = "certificate is on hold";
-+        break;
- 
--          case GNUTLS_X509_CRLREASON_AACOMPROMISE:
--            crl_reason = "AA compromised";
--            break;
--        }
-+      case GNUTLS_X509_CRLREASON_REMOVEFROMCRL:
-+        crl_reason = "will be removed from delta CRL";
-+        break;
- 
--        failf(data, "Server certificate was revoked: %s", crl_reason);
-+      case GNUTLS_X509_CRLREASON_PRIVILEGEWITHDRAWN:
-+        crl_reason = "privilege withdrawn";
-         break;
--      }
- 
--      default:
--      case GNUTLS_OCSP_CERT_UNKNOWN:
--        failf(data, "Server certificate status is unknown");
-+      case GNUTLS_X509_CRLREASON_AACOMPROMISE:
-+        crl_reason = "AA compromised";
-         break;
-       }
- 
--      gnutls_ocsp_resp_deinit(ocsp_resp);
-+      failf(data, "Server certificate was revoked: %s", crl_reason);
-+      break;
-+    }
- 
--      return CURLE_SSL_INVALIDCERTSTATUS;
-+    default:
-+    case GNUTLS_OCSP_CERT_UNKNOWN:
-+      failf(data, "Server certificate status is unknown");
-+      break;
-     }
--    else
--      infof(data, "  server certificate status verification OK");
-+
-+    gnutls_ocsp_resp_deinit(ocsp_resp);
-+    if(status != GNUTLS_OCSP_CERT_GOOD)
-+      return CURLE_SSL_INVALIDCERTSTATUS;
-   }
-   else
-     infof(data, "  server certificate status verification SKIPPED");
