The H block cells and hospital where republican hunger strikers like Bobby Sands died should be flattened, some unionists claim.
A petition calling for prison buildings at the Maze site to be de-listed and demolished and a controversial peace centre relocated has been launched.
In a joint statement Ulster Unionist Party leader Mike Nesbitt and UUP Fermanagh MLA Tom Elliott, Jim Allister of the TUV and David McNarry from Ukip demanded an immediate halt to the contentious development project which was given the go-ahead last week.
"Over the course of a number of months we met and listened to innocent victims groups right across Northern Ireland. It is clear that there is significant opposition within these groups, the RUC George Cross Association, the Prison Officers Association and other organisations to the conflict transformation centre being built at the Maze and the retention of the hospital and H-Blocks.
"The Maze site is the wrong location for a peace centre where the whole focus will be on the prison and what happened within its walls. The DUP and Sinn Fein should move the centre to another site so that the Maze redevelopment can go ahead unhindered by the toxic legacy of our past," the statement said.
Hundreds of republican and loyalist paramilitary prisoners were held at the Maze, near Lisburn in Co Antrim, between 1971 and 2000.
In 1974 republicans embarked in a campaign to gain political status and refused to wear prison clothes.
By 1978 many had progressed to a no-wash or dirty protest in their effort for special category status.
Ten men, including Bobby Sands who had been elected as MP for Fermanagh South Tyrone, starved to death at the prison during the 1981 republican hunger strikes.