That has put him in a standoff with MPs who want Labour's disastrous result analysed before the leadership is decided. They are aiming for about six months' delay - something senior Labour figures such as Sir Michael Cullen are understood to be urging.
In an indication his fellow MPs had dug their heels in, Mr Cunliffe would not rule out resigning to force the contest rather than wait for caucus to hold a confidence motion. Earlier in the day he had said he had no intention of resigning.
The tension between Mr Cunliffe and Labour's more centrist MPs angered by his apparent refusal to take blame has intensified after Mr Cunliffe tried to muzzle MPs from talking publicly and several ignored his edict. Mr Cunliffe said he did take responsibility for the loss, but would not apologise to his caucus because he had personally performed well.
There was an extraordinary exchange earlier in the day through the media after Mr Cunliffe said former leader David Shearer was "positioning" to contest the leadership by refusing to abide by a gagging order on Labour MPs. Mr Shearer has not ruled out a challenge.
Mr Cunliffe's rivals have accused him of positioning in return, saying he was using the situation as a platform for his own ambition by muzzling other MPs and trying to railroad them into a quick contest before the scale of Labour's loss under his leadership could sink in with the wider membership. However, there was also flak going the other way by MPs disappointed that Mr Shearer and others, including Stuart Nash, were speaking publicly.
In a clear attempt to show he had strong backing, Mr Cunliffe was flanked by his core support group at his early press conference - Nanaia Mahuta, Louisa Wall, Iain Lees-Galloway, Carmel Sepuloni and Sue Moroney.
In a further sign Mr Cunliffe was losing his grip on the caucus, loyalist Ms Moroney resigned as chief whip and was replaced by Cunliffe critic Chris Hipkins, although Ms Sepuloni was appointed deputy. Mr Cunliffe's deputy leader David Parker is yet to rule out a challenge against Mr Cunliffe.
Where to from here?
To trigger a wider party vote on his leadership, Mr Cunliffe would have to resign as leader or fail a confidence vote in caucus.
• Camp Cunliffe: David Cunliffe, Iain Lees-Galloway, Nanaia Mahuta, Sue Moroney, Carmel Sepuloni, Su'a William Sio, Louisa Wall.
• Another candidate: Jacinda Ardern, David Clark, Clayton Cosgrove, Clare Curran, Kelvin Davis, Ruth Dyson, Kris Faafoi, Phil Goff, Chris Hipkins, Annette King, Andrew Little, Trevor Mallard, Stuart Nash, Damien O'Connor, David Parker, Grant Robertson, David Shearer, Rino Tirikatene, Phil Twyford, Megan Woods.
• Unknown: Peeni Henare, Adrian Rurawhe, Jenny Salesa, Meka Whaitiri, Poto Williams.
• Possible contenders: David Cunliffe, Grant Robertson, Stuart Nash, David Shearer, David Parker.
