diff --git a/imagebuildah/stage_executor.go b/imagebuildah/stage_executor.go
index fcab73c778..3928457f59 100644
--- a/imagebuildah/stage_executor.go
+++ b/imagebuildah/stage_executor.go
@@ -2113,12 +2113,19 @@ func (s *StageExecutor) tagExistingImage(ctx context.Context, cacheID, output st
 		return "", nil, fmt.Errorf("getting source imageReference for %q: %w", cacheID, err)
 	}
 	options := cp.Options{
-		RemoveSignatures: true, // more like "ignore signatures", since they don't get removed when src and dest are the same image
+		RemoveSignatures:     true, // more like "ignore signatures", since they don't get removed when src and dest are the same image
+		DestinationTimestamp: s.executor.timestamp,
 	}
 	manifestBytes, err := cp.Image(ctx, policyContext, dest, src, &options)
 	if err != nil {
 		return "", nil, fmt.Errorf("copying image %q: %w", cacheID, err)
 	}
+
+	// If the destination isn't container storage, then we're done and can return early
+	if dest.Transport().Name() != is.Transport.Name() {
+		return cacheID, nil, nil
+	}
+
 	manifestDigest, err := manifest.Digest(manifestBytes)
 	if err != nil {
 		return "", nil, fmt.Errorf("computing digest of manifest for image %q: %w", cacheID, err)
diff --git a/tests/bud.bats b/tests/bud.bats
index c67b4fc8ab..3d2a27319f 100644
--- a/tests/bud.bats
+++ b/tests/bud.bats
@@ -7856,6 +7856,17 @@ _EOF
   diff "${outpath}.b" "${outpath}.c"
 }
 
+@test "build-with-timestamp-applies-to-oci-archive-with-base" {
+  local outpath="${TEST_SCRATCH_DIR}/timestamp-oci.tar"
+
+  run_buildah build -f <(echo 'FROM busybox') --tag=oci-archive:${outpath}.a --timestamp 0
+  sleep 1.1 # sleep at least 1 second, so that timestamps are incremented
+  run_buildah build -f <(echo 'FROM busybox') --tag=oci-archive:${outpath}.b --timestamp 0
+
+  # should be the same
+  diff "${outpath}.a" "${outpath}.b"
+}
+
 @test "bud-source-date-epoch-arg" {
   _prefetch busybox
   local timestamp=60