diff --git a/library/psa_crypto.c b/library/psa_crypto.c
index c28491e66f..2bbe3a5a78 100644
--- a/library/psa_crypto.c
+++ b/library/psa_crypto.c
@@ -3932,6 +3932,34 @@ uint32_t mbedtls_psa_verify_hash_get_num_ops(
         * defined( MBEDTLS_ECP_RESTARTABLE ) */
 }
 
+/* Detect supported interruptible sign/verify mechanisms precisely.
+ * This is not strictly needed: we could accept everything, and let the
+ * code fail later during complete() if the mechanism is unsupported
+ * (e.g. attempting deterministic ECDSA when only the randomized variant
+ * is available). But it's easier for applications and especially for our
+ * test code to detect all not-supported errors during start().
+ *
+ * Note that this function ignores the hash component. The core code
+ * is supposed to check the hash part by calling is_hash_supported().
+ */
+static inline int can_do_interruptible_sign_verify(psa_algorithm_t alg)
+{
+#if defined(MBEDTLS_ECP_RESTARTABLE)
+#if defined(MBEDTLS_PSA_BUILTIN_ALG_DETERMINISTIC_ECDSA)
+    if (PSA_ALG_IS_DETERMINISTIC_ECDSA(alg)) {
+        return 1;
+    }
+#endif
+#if defined(MBEDTLS_PSA_BUILTIN_ALG_ECDSA)
+    if (PSA_ALG_IS_RANDOMIZED_ECDSA(alg)) {
+        return 1;
+    }
+#endif
+#endif /* defined(MBEDTLS_ECP_RESTARTABLE) */
+    (void) alg;
+    return 0;
+}
+
 psa_status_t mbedtls_psa_sign_hash_start(
     mbedtls_psa_sign_hash_interruptible_operation_t *operation,
     const psa_key_attributes_t *attributes, const uint8_t *key_buffer,
@@ -3945,7 +3973,7 @@ psa_status_t mbedtls_psa_sign_hash_start(
         return PSA_ERROR_NOT_SUPPORTED;
     }
 
-    if (!PSA_ALG_IS_ECDSA(alg)) {
+    if (!can_do_interruptible_sign_verify(alg)) {
         return PSA_ERROR_NOT_SUPPORTED;
     }
 
@@ -4161,7 +4189,7 @@ psa_status_t mbedtls_psa_verify_hash_start(
         return PSA_ERROR_NOT_SUPPORTED;
     }
 
-    if (!PSA_ALG_IS_ECDSA(alg)) {
+    if (!can_do_interruptible_sign_verify(alg)) {
         return PSA_ERROR_NOT_SUPPORTED;
     }
 
diff --git a/tests/suites/test_suite_psa_crypto.data b/tests/suites/test_suite_psa_crypto.data
index f7bbbc7ee0..609cdbadae 100644
--- a/tests/suites/test_suite_psa_crypto.data
+++ b/tests/suites/test_suite_psa_crypto.data
@@ -4489,11 +4489,11 @@ sign_hash_fail_interruptible:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_SECP_R1):"
 
 PSA sign hash int (ops=inf): det ECDSA not supported
 depends_on:!PSA_WANT_ALG_DETERMINISTIC_ECDSA:PSA_WANT_ALG_ECDSA:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_BASIC:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_IMPORT:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_EXPORT:PSA_WANT_ECC_SECP_R1_384
-sign_hash_fail_interruptible:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_SECP_R1):"3f5d8d9be280b5696cc5cc9f94cf8af7e6b61dd6592b2ab2b3a4c607450417ec327dcdcaed7c10053d719a0574f0a76a":PSA_ALG_DETERMINISTIC_ECDSA( PSA_ALG_SHA_256 ):"2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824":96:PSA_SUCCESS:PSA_ERROR_NOT_SUPPORTED:PSA_INTERRUPTIBLE_MAX_OPS_UNLIMITED
+sign_hash_fail_interruptible:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_SECP_R1):"3f5d8d9be280b5696cc5cc9f94cf8af7e6b61dd6592b2ab2b3a4c607450417ec327dcdcaed7c10053d719a0574f0a76a":PSA_ALG_DETERMINISTIC_ECDSA( PSA_ALG_SHA_256 ):"2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824":96:PSA_ERROR_NOT_SUPPORTED:PSA_ERROR_BAD_STATE:PSA_INTERRUPTIBLE_MAX_OPS_UNLIMITED
 
 PSA sign hash int (ops=min): det ECDSA not supported
 depends_on:!PSA_WANT_ALG_DETERMINISTIC_ECDSA:PSA_WANT_ALG_ECDSA:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_BASIC:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_IMPORT:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_EXPORT:PSA_WANT_ECC_SECP_R1_384
-sign_hash_fail_interruptible:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_SECP_R1):"3f5d8d9be280b5696cc5cc9f94cf8af7e6b61dd6592b2ab2b3a4c607450417ec327dcdcaed7c10053d719a0574f0a76a":PSA_ALG_DETERMINISTIC_ECDSA( PSA_ALG_SHA_256 ):"2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824":96:PSA_SUCCESS:PSA_ERROR_NOT_SUPPORTED:0
+sign_hash_fail_interruptible:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_SECP_R1):"3f5d8d9be280b5696cc5cc9f94cf8af7e6b61dd6592b2ab2b3a4c607450417ec327dcdcaed7c10053d719a0574f0a76a":PSA_ALG_DETERMINISTIC_ECDSA( PSA_ALG_SHA_256 ):"2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824":96:PSA_ERROR_NOT_SUPPORTED:PSA_ERROR_BAD_STATE:0
 
 PSA sign/verify hash: RSA PKCS#1 v1.5, raw
 depends_on:PSA_WANT_ALG_RSA_PKCS1V15_SIGN:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_BASIC:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_IMPORT