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He said that he would expect the same in return if he was successful in staying on.
His comments indicate he will not leave Parliament altogether if he is ousted as leader - something he has refused to confirm until now.
Mr Cunliffe said Labour's result was terrible and he took responsibility for that. "The voters are never wrong. We work hard but we are not yet seen as a credible alternative."
Watch: Cunliffe: 'Not a good result'
He said there were a variety of mechanisms to trigger the leadership contest - one included his resignation but he would not take that option. That would leave it to caucus to to hold a vote of no confidence in him to trigger one - but he said he would not call for one himself.
That vote must be held within three months - but Mr Cunliffe said he believed it should happen as soon as possible and before the final results were known even if it was He said one MP would not make much difference in a confidence vote.
After avoiding the media all day yesterday, Mr Cunliffe held a press conference this morning, also using it as an opportunity to introduce Labour's new MPs before moving on to talk about his leadership. Mr Cunliffe said the presence of new MPs was a bright spot in what had been a terrible loss for Labour.
Mr Cunliffe is about to go in to the first caucus meeting after leading Labour to its worst trouncing in 80 years.
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When conceding on election night, he announced he intended to seek a new mandate to change the party and lead it into the 2017 election.
Several MPs this morning said there should be no rush into a leadership contest and have pushed for a review of the party's performance before any changes.
He said his colleagues' calls to wait at least until the final count was known were "positioning."
"I think there's a bit of positioning going on and people can see that for what it is."
Several Labour MPs show open defiance
Several Labour MPs showed open defiance to Mr Cunliffe's attempt to silence them within minutes of his own press conference - David Shearer and Phil Goff, and MPs Damien O'Connor and Clayton Cosgrove all stopped to talk to media again on their way into Labour's caucus.
Mr Shearer said he would not abide by Mr Cunliffe's instruction. He said as former leader he had a right to say what he believed Labour should be doing.
"What I don't feel is that I should be silent when we need to be acknowledging our defeat. I've got skin in the game here. For two of the last three years I was the leader and all I am doing is speaking very candidly about the way we should go forward which is to own our defeat and move forward on that basis."
Mr Goff was less combative, but agreed with Mr Shearer that Labour should wait until it had analysed what went wrong before moving on the leadership.
He said he would wait to hear what Mr Cunliffe had to say. "We need to be honest, we need to show some humility about the scale of that defeat, to address what we think led to that defeat and then unite. I hope it will be a calm and clear look at what we need to do to re-win the confidence of the big section of the electorate necessary for us to take government."
Mr O'Connor said he was not a great fan of Labour's new primary-style method of choosing the leader. "I think the last one we had didn't necessarily deliver the best outcome."