Latest "Vietnam veterans benefits" stories
Veterans Affairs officials won't start processing the cases until next January, upsetting some advocates.
The measure had been stalled on Capitol Hill for several weeks, as court moves took precedence for advocates.
The high court extended the appeals deadline on the issue for 30 days, although Department of Justice officials have not said if they will pursue one.
Lawmakers are planning a flurry of moves to address the issue of the Vietnam veterans benefits in coming weeks.