Communities Minister Gordon Lyons has called for the full reinstatement of the winter fuel payment and said an increase on those eligible "would not go far enough".
In a U-turn following mounting political pressure in recent weeks, the Prime Minister Sir Keir Starmer announced plans to ease cuts to winter fuel payments.
Around 250,000 people here missed out on the winter fuel payment last year after Northern Ireland followed a Westminster decision to make the payments means-tested.
On Wednesday, Lyons welcomed the government's realisation that an "error" was made and urged for the return of the "universal winter fuel payment that protects all pensioners".