Jim Allister has said he will let the electorate decide in a battle for the North Antrim Westminster seat.
Mr Allister indicated he intends to challenge Ian Paisley's seat after the performance of Traditional Unionist Voice in the European election.
On Wednesday, the DUP MP issued a challenge to the TUV leader.
Speaking from Westminster, Mr Paisley said his former DUP colleague was "very welcome to come and get a hiding in North Antrim".
Mr Paisley said although the TUV polled well in the European elections, his party was still defeated by the DUP.
He said: "The election was won because he didn't get a seat.
"He stole the seat from me, Jim Allister had not political breath except for what he took from me."
Speaking to the BBC on Thursday Mr Allister said the former DUP leader's words were "hollow".
"Ian Paisley tries to claim it as a triumph. He says there was no defeat, everyone knows there was a defeat," he said.
"If the DUP are in the business of sleepwalking out of Monday into the future, well I'm quite content that the good people of North Antrim and elsewhere will continue to give us the resounding type of result there was on Monday.
"What we need is a system where you can have opposition, people who are both in and out of government.
"A voluntary coalition where those that are in government are bound by policies that they all support."
Traditional Unionist Voice took almost 70,000 votes from the DUP.