diff --git a/var/spack/repos/builtin/packages/libzmq/package.py b/var/spack/repos/builtin/packages/libzmq/package.py
index e994fd74c2..dac309b699 100644
--- a/var/spack/repos/builtin/packages/libzmq/package.py
+++ b/var/spack/repos/builtin/packages/libzmq/package.py
@@ -64,13 +64,20 @@ class Libzmq(AutotoolsPackage):
     depends_on("libunwind", when="+libunwind")
 
     conflicts("%gcc@8:", when="@:4.2.2")
-    conflicts("%gcc@12:", when="@4.3.2:4.3.4")
+    conflicts("%gcc@11:", when="@:4.3.2")
 
     # Fix aggressive compiler warning false positive
     patch(
         "https://github.com/zeromq/libzmq/commit/92b2c38a2c51a1942a380c7ee08147f7b1ca6845.patch?full_index=1",
         sha256="310b8aa57a8ea77b7ac74debb3bf928cbafdef5e7ca35beaac5d9c61c7edd239",
-        when="@4.2.3:4.3.4 %gcc@11:",
+        when="@4.3.3:4.3.4 %gcc@11:",
+    )
+
+    # Fix build issues with gcc-12
+    patch(
+        "https://github.com/zeromq/libzmq/pull/4334.patch?full_index=1",
+        sha256="edca864cba914481a5c97d2e975ba64ca1d2fbfc0044e9a78c48f1f7b2bedb6f",
+        when="@4.3.4 %gcc@12:",
     )
 
     def url_for_version(self, version):