The caucus was "not at that point" of having a confidence vote about his leadership.
"We have all made a decision that we've got a number of issues to consider and we won't be commenting on our confidential caucus discussions either now or in the future."
Asked whether any of his colleagues had declared they would stand against him for the leadership, Mr Cunliffe said "I'm not at liberty to discuss the caucus".
"I've said all I can say at the moment which is that we have had a range of discussions we've got a range of things to think about, we'll be continuing those discussions at the next caucus meeting."
Mr Cunliffe said the review of the party's election campaign would likely be conducted by two or more senior and qualified figures appointed by the party's council.
Earlier today, Mr Cunliffe called again for an early leadership contest and pledged to get behind whoever wins if he loses.
Flanked by his deputy David Parker, Mr Cunliffe said the party's ruling Council would launch an immediate review of the election today, but Labour had to get on with rebuilding as soon as possible.
"Uncertainty is deeply damaging to the party."
"We must stop the leaks, we must stop the infighting. It's not good enough. We need a leader confirmed for the caucus and party to get on. That leader may or may not be me."
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."