diff --git a/guix/build/download.scm b/guix/build/download.scm
index c08221b3b2..23c9a4d466 100644
--- a/guix/build/download.scm
+++ b/guix/build/download.scm
@@ -268,7 +268,10 @@ host name without trailing dot."
     ;; "(gnutls) Priority Strings"); see <http://bugs.gnu.org/23311>.
     ;; Explicitly disable SSLv3, which is insecure:
     ;; <https://tools.ietf.org/html/rfc7568>.
-    (set-session-priorities! session "NORMAL:%COMPAT:-VERS-SSL3.0")
+    ;;
+    ;; FIXME: Since we currently fail to handle TLS 1.3, remove it; see
+    ;; <https://bugs.gnu.org/34102>.
+    (set-session-priorities! session "NORMAL:%COMPAT:-VERS-SSL3.0:-VERS-TLS1.3")
 
     (set-session-credentials! session
                               (if (and verify-certificate? ca-certs)