diff --git a/src/dune_rules/cram/cram_lexer.mll b/src/dune_rules/cram/cram_lexer.mll
index 7ad86800c1d..a88b61243d0 100644
--- a/src/dune_rules/cram/cram_lexer.mll
+++ b/src/dune_rules/cram/cram_lexer.mll
@@ -135,9 +135,13 @@ and command_cont loc acc = parse
   | "  > " ([^'\n']* as str)
     { let loc = Loc.set_stop loc (Lexing.lexeme_end_p lexbuf) in
       eol_then_continue_or_finish loc str acc lexbuf }
-  | "  >"
+  | "  >" '\n'
+    { let loc = Loc.set_stop loc (pos_before_newline lexbuf) in
+      Lexing.new_line lexbuf;
+      command_cont loc ("" :: acc) lexbuf }
+  | "  >" eof
     { let loc = Loc.set_stop loc (Lexing.lexeme_end_p lexbuf) in
-      eol_then_continue_or_finish loc "" acc lexbuf }
+      (loc, Command (List.rev ("" :: acc))) }
   | ""
     { (loc, Command (List.rev acc)) }
 
diff --git a/test/blackbox-tests/test-cases/cram/conflict-marker-lexer-error.t b/test/blackbox-tests/test-cases/cram/conflict-marker-lexer-error.t
deleted file mode 100644
index ac56e79ea9f..00000000000
--- a/test/blackbox-tests/test-cases/cram/conflict-marker-lexer-error.t
+++ /dev/null
@@ -1,13 +0,0 @@
-
-  $ cat >dune-project <<EOF
-  > (lang dune 3.21)
-  > EOF
-
-  $ cat > t1.t <<'EOF'
-  >   $ echo '>> Hello'
-  >   >> Hello
-  > EOF
-  $ dune runtest 2>&1 | grep -i "\(I must not crash\|exn =\)"
-     { exn = "Failure(\"lexing: empty token\")" })
-  I must not crash.  Uncertainty is the mind-killer. Exceptions are the
-
diff --git a/test/expect-tests/dune_rules/cram_parsing_tests.ml b/test/expect-tests/dune_rules/cram_parsing_tests.ml
index 5cfe28b1365..0847d048bf2 100644
--- a/test/expect-tests/dune_rules/cram_parsing_tests.ml
+++ b/test/expect-tests/dune_rules/cram_parsing_tests.ml
@@ -473,3 +473,21 @@ let%expect_test "single-space comment after output" =
     }
     |}]
 ;;
+
+(* Test for https://github.com/ocaml/dune/pull/12963: >> in output confused the
+   lexer *)
+let%expect_test "output resembling conflict marker" =
+  test "  $ echo '>> Hello'\n  >> Hello";
+  [%expect
+    {|
+    File "test.t", line 1, characters 2-19:
+    1 |   $ echo '>> Hello'
+          ^^^^^^^^^^^^^^^^^
+
+    Command [ "echo '>> Hello'" ]
+    { pos_fname = "test.t"
+    ; start = { pos_lnum = 1; pos_bol = 0; pos_cnum = 2 }
+    ; stop = { pos_lnum = 1; pos_bol = 0; pos_cnum = 19 }
+    }
+    |}]
+;;