diff --git a/ChangeLog.d/fix-tls12-rsa-pss-sigalgs.txt b/ChangeLog.d/fix-tls12-rsa-pss-sigalgs.txt
new file mode 100644
index 0000000000..34296b602e
--- /dev/null
+++ b/ChangeLog.d/fix-tls12-rsa-pss-sigalgs.txt
@@ -0,0 +1,4 @@
+Bugfix
+   * Fix a TLS 1.2 regression that caused clients to reject valid
+     ServerKeyExchange signatures using RSA-PSS signature algorithms.
+     Fixes #10668.
diff --git a/library/ssl_tls12_client.c b/library/ssl_tls12_client.c
index a0170d51f6..c101ccd91e 100644
--- a/library/ssl_tls12_client.c
+++ b/library/ssl_tls12_client.c
@@ -12,6 +12,7 @@
 #include "mbedtls/platform.h"
 
 #include "mbedtls/ssl.h"
+#include "ssl_debug_helpers.h"
 #include "ssl_client.h"
 #include "debug_internal.h"
 #include "mbedtls/error.h"
@@ -1742,32 +1743,77 @@ static int ssl_parse_signature_algorithm(mbedtls_ssl_context *ssl,
 {
     if (mbedtls_ssl_get_pk_sigalg_and_md_alg_from_sig_alg(sig_alg, pk_alg, md_alg) != 0) {
         MBEDTLS_SSL_DEBUG_MSG(1,
-                              ("Server used unsupported value in SigAlg extension 0x%04x",
-                               sig_alg));
+                              ("Server used unsupported %s signature algorithm",
+                               mbedtls_ssl_sig_alg_to_str(sig_alg)));
         return MBEDTLS_SSL_ALERT_MSG_ILLEGAL_PARAMETER;
     }
 
     /*
-     * mbedtls_ssl_get_pk_sigalg_and_md_alg_from_sig_alg() understands sig_alg code points across
-     * TLS versions. Make sure that the received sig_alg extension is valid in TLS 1.2.
+     * mbedtls_ssl_get_pk_sigalg_and_md_alg_from_sig_alg() understands
+     * signature algorithm code points from both TLS 1.2 and TLS 1.3. Make sure
+     * that the selected signature algorithm is acceptable when TLS 1.2 is
+     * negotiated.
+     *
+     * In TLS 1.2, RSA-PSS signature algorithms (rsa_pss_rsae_*) are not
+     * defined by RFC 5246. However, RFC 8446 Section 4.2.3 requires that
+     * implementations which advertise support for RSASSA-PSS must be
+     * prepared to accept such signatures even when TLS 1.2 is negotiated,
+     * provided they were offered in the signature_algorithms extension.
+     *
+     * Therefore, we allow rsa_pss_rsae_* here if:
+     *  - the implementation supports them, and
+     *  - they were offered in the signature_algorithms extension (checked by
+     *    `mbedtls_ssl_sig_alg_is_offered()` below).
+     *
+     * If we were to add full support for rsa_pss_rsae_* signature algorithms
+     * in TLS 1.2 (not defined by RFC 5246; RFC 8446 requires implementations
+     * that advertise RSASSA-PSS to accept such signatures even when TLS 1.2
+     * is negotiated; in practice, several TLS implementations also offer and
+     * use these algorithms in TLS 1.2-only configurations), we should then
+     * integrate RSA-PSS into the TLS 1.2 signature algorithm support logic
+     * (`mbedtls_ssl_tls12_sig_alg_is_supported()`) instead of handling it as a
+     * special case here.
      */
     if (!mbedtls_ssl_sig_alg_is_supported(ssl, sig_alg)) {
-        MBEDTLS_SSL_DEBUG_MSG(1,
-                              ("Server used unsupported value in SigAlg extension 0x%04x",
-                               sig_alg));
-        return MBEDTLS_SSL_ALERT_MSG_ILLEGAL_PARAMETER;
+        switch (sig_alg) {
+#if defined(PSA_WANT_ALG_RSA_PSS)
+#if defined(PSA_WANT_ALG_SHA_256)
+            case MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA256:
+#endif
+#if defined(PSA_WANT_ALG_SHA_384)
+            case MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA384:
+#endif
+#if defined(PSA_WANT_ALG_SHA_512)
+            case MBEDTLS_TLS1_3_SIG_RSA_PSS_RSAE_SHA512:
+#endif
+#if defined(PSA_WANT_ALG_SHA_256) || defined(PSA_WANT_ALG_SHA_384) || defined(PSA_WANT_ALG_SHA_512)
+        MBEDTLS_SSL_DEBUG_MSG(3,
+                              (
+                                  "Accepting TLS 1.2 RSA-PSS signature algorithm %s via compatibility exception",
+                                  mbedtls_ssl_sig_alg_to_str(sig_alg)));
+        break;
+#endif
+#endif /* PSA_WANT_ALG_RSA_PSS */
+            default:
+                MBEDTLS_SSL_DEBUG_MSG(1,
+                                      ("Server used unsupported %s signature algorithm",
+                                       mbedtls_ssl_sig_alg_to_str(sig_alg)));
+                return MBEDTLS_SSL_ALERT_MSG_ILLEGAL_PARAMETER;
+        }
     }
 
     /*
      * Check if the signature algorithm is acceptable
      */
     if (!mbedtls_ssl_sig_alg_is_offered(ssl, sig_alg)) {
-        MBEDTLS_SSL_DEBUG_MSG(1, ("Server used SigAlg value 0x%04x that was not offered", sig_alg));
+        MBEDTLS_SSL_DEBUG_MSG(1,
+                              ("Server used the signature algorithm %s that was not offered",
+                               mbedtls_ssl_sig_alg_to_str(sig_alg)));
         return MBEDTLS_SSL_ALERT_MSG_ILLEGAL_PARAMETER;
     }
 
-    MBEDTLS_SSL_DEBUG_MSG(2, ("Server used SignatureAlgorithm %d", sig_alg & 0x00FF));
-    MBEDTLS_SSL_DEBUG_MSG(2, ("Server used HashAlgorithm %d", sig_alg >> 8));
+    MBEDTLS_SSL_DEBUG_MSG(2, ("Server used the signature algorithm %s",
+                              mbedtls_ssl_sig_alg_to_str(sig_alg)));
 
     return 0;
 }
diff --git a/tests/ssl-opt.sh b/tests/ssl-opt.sh
index 47ff800ed1..4a4ee4d1ef 100755
--- a/tests/ssl-opt.sh
+++ b/tests/ssl-opt.sh
@@ -13938,7 +13938,6 @@ run_test    "TLS 1.2: Check rsa_pss_rsae compatibility issue, m->O" \
             -c "Protocol is TLSv1.2" \
             -c "HTTP/1.0 200 [Oo][Kk]"
 
-
 requires_gnutls_tls1_3
 requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
 requires_config_enabled MBEDTLS_DEBUG_C
@@ -13954,6 +13953,43 @@ run_test    "TLS 1.2: Check rsa_pss_rsae compatibility issue, m->G" \
             -c "Protocol is TLSv1.2" \
             -c "HTTP/1.0 200 [Oo][Kk]"
 
+requires_openssl_tls1_3_with_compatible_ephemeral
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled PSA_WANT_ALG_RSA_PSS
+requires_config_enabled PSA_WANT_ALG_SHA_256
+run_test    "TLS 1.2: Server forces TLS 1.2 and rsa_pss_rsae_sha256, m->O" \
+            "$O_NEXT_SRV_NO_CERT -cert $DATA_FILES_PATH/server2-sha256.crt -key $DATA_FILES_PATH/server2.key
+                                 -tls1_2 -sigalgs rsa_pss_rsae_sha256 " \
+            "$P_CLI debug_level=3" \
+            0 \
+            -c "sent signature scheme \\[804\\] rsa_pss_rsae_sha256" \
+            -c "Perform .* computation of digest of ServerKeyExchange" \
+            -c "Server used the signature algorithm rsa_pss_rsae_sha256" \
+            -c "Protocol is TLSv1.2" \
+            -c "HTTP/1.0 200 [Oo][Kk]"
+
+requires_gnutls_tls1_3
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_2
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_3
+requires_config_enabled MBEDTLS_DEBUG_C
+requires_config_enabled MBEDTLS_SSL_CLI_C
+requires_config_enabled PSA_WANT_ALG_RSA_PSS
+requires_config_enabled PSA_WANT_ALG_SHA_256
+run_test    "TLS 1.2: Server forces TLS 1.2 and rsa_pss_rsae_sha256, m->G" \
+            "$G_NEXT_SRV_NO_CERT --x509certfile $DATA_FILES_PATH/server2-sha256.crt --x509keyfile $DATA_FILES_PATH/server2.key
+                    --disable-client-cert
+                    --priority=NORMAL:-VERS-ALL:+VERS-TLS1.2:-SIGN-ALL:+SIGN-RSA-PSS-RSAE-SHA256" \
+            "$P_CLI debug_level=3" \
+            0 \
+            -c "sent signature scheme \\[804\\] rsa_pss_rsae_sha256" \
+            -c "Perform .* computation of digest of ServerKeyExchange" \
+            -c "Server used the signature algorithm rsa_pss_rsae_sha256" \
+            -c "Protocol is TLSv1.2" \
+            -c "HTTP/1.0 200 [Oo][Kk]"
+
 requires_config_enabled MBEDTLS_SSL_SRV_C
 requires_config_enabled MBEDTLS_DEBUG_C
 requires_config_enabled MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_EPHEMERAL_ENABLED