Michael Hayes told the BBC he defused a third bomb on the night 21 people lost their lives.
He said he accepts "collective responsibility" for all of the group's actions in the Birmingham pub bombings.
The Labour MP for Birmingham Perry Barr, Khalid Mahmood, said the families continued to "suffer".
Speaking to the BBC's Sunday Politics programme, Mr Mahmood said: "If this happened anywhere else in the world, they'd leave no stone unturned to deal with this, but here we are forgetting about all the citizens of Birmingham that lost their lives.
"We should ask him to be brought here and to be questioned properly."
Mr Mahmood said an application needs to be made to the Irish government to bring Michael Hayes over for questioning.
Jess Phillips, the Labour MP for Birmingham Yardley, said she would be calling on the prime minister to have Mr Hayes extradited.
"If he's going to make these claims he should be called in to questioned in by the police.
"Otherwise it's as if he's speaking with impunity and the people who died it doesn't matter and there's no investigations into their deaths."
Lord (Digby) Jones of Birmingham said: "I'm left with the feeling that if this was happening in one or two other cities in Britain there would be an enormous call for all this.
"I just think (he is) innocent until proven guilty... but clearly that guy has questions to answer.
"I think it's incumbent for us as a society to say to that man now, you have said this to camera. Come and justify yourself and help us."
West Midlands Police said last week its investigation remained open and it would respond to any new significant information to bring those responsible to justice.
A UK Government spokesperson said it does not comment on individual cases.
Birmingham MPs are calling for a self-confessed IRA bomb-maker to be extradited and face questioning by police.