diff --git a/core/core.el b/core/core.el
index 94739aafd..eec32a36d 100644
--- a/core/core.el
+++ b/core/core.el
@@ -191,9 +191,12 @@ users).")
 ;; least a little more discerning.
 (setq gnutls-verify-error (not (getenv "INSECURE"))
       gnutls-algorithm-priority
-      (concat "SECURE128:+SECURE192:-VERS-ALL:+VERS-TLS1.2"
-              (if (ignore-errors (>= libgnutls-version 30605))
-                ":+VERS-TLS1.3"))
+      (when (boundp 'libgnutls-version)
+        (concat "SECURE128:+SECURE192:-VERS-ALL:+VERS-TLS1.2"
+                (if (and (not IS-WINDOWS)
+                         (not (version< emacs-version "26.3"))
+                         (>= libgnutls-version 30605))
+                    ":+VERS-TLS1.3")))
       ;; `gnutls-min-prime-bits' is set based on recommendations from
       ;; https://www.keylength.com/en/4/
       gnutls-min-prime-bits 3072