diff --git a/fs/operations/multithread.go b/fs/operations/multithread.go
index 24725b355..582df8445 100644
--- a/fs/operations/multithread.go
+++ b/fs/operations/multithread.go
@@ -6,6 +6,7 @@ import (
 	"errors"
 	"fmt"
 	"io"
+	"time"
 
 	"github.com/rclone/rclone/fs"
 	"github.com/rclone/rclone/fs/accounting"
@@ -253,6 +254,9 @@ func multiThreadCopy(ctx context.Context, f fs.Fs, remote string, src fs.Object,
 				if err != nil {
 					return nil, fmt.Errorf("multi-thread copy: failed to read metadata from source object: %w", err)
 				}
+				if _, foundMeta := meta["mtime"]; !foundMeta {
+					meta.Set("mtime", src.ModTime(ctx).Format(time.RFC3339Nano))
+				}
 				err = do.SetMetadata(ctx, meta)
 				if err != nil {
 					return nil, fmt.Errorf("multi-thread copy: failed to set metadata: %w", err)