The legislation, called the “Stop Sanctuary Cities Act,” had been scheduled to be marked up in the Senate Judiciary Committee on Thursday. It was a long-awaited session — the markup had been scheduled for the Thursday before August recess, until the Senate adjourned a few days early.

But a committee spokeswoman said Tuesday that it would be further delayed.

“The members are still working on improving the language, so it will be held over,” Beth Levine, a spokeswoman for Chairman Chuck Grassley (R-Iowa), said Tuesday.