Rimutaka MP Chris Hipkins also wanted it to be a private conversation within the party.
"One of the clear messages from New Zealanders is they are sick and tired of the Labour Party talk about itself. We need to get out there and re-connect with New Zealanders and so now's the time we need to hunker down.
"I don't think we should be airing our dirty laundry in public. I think New Zealanders have had a gutsful of that."
It was time to come together to reflect quite soberly on the outcome of the election, which was a very bad result, and work out how to move forward in a way that is going to reconnect the Labour Party with all New Zealanders.
"We have previously had over a million people voting for us. We got half a million people voting for us. We need to reconnect with half a million people who used to vote Labour and now vote for someone else."
The newly elected MP for Napier, Stuart Nash, who has not ruled out a challenge for the top job himself, said he supported any leader who was the Labour leader "until they day they are not the Labour leader."
Labour list MP Clayton Cosgrove said Labour needed "cool heads."
"The people of New Zealand have sent us a message and they should be respected and I think it would smack of arrogance of the highest order if we were to rush through a process ... and getting the message and reviewing what happened and dealing with that and then looking calmly and coolly at any next steps."
He said thousands of New Zealanders who once voted for Labour did not feel it was a broad-based party.
"They feel we are a narrow party with very little in common with them and they are right," he said.
"There is a feeling and I think it is inarguable that we are a narrow party, that we represent narrow interests, that we get tied up in peripheral stuff."
"The voters' needs and concerns change. Some people who were wage workers are now contract worker.
"Those contract workers now have priorities as small businesses, priorities like provisional tax, GST and others. If we as a political movement don't change and evolve with then we have some difficulties. We fall out of touch."
Dunedin South MP Claire Curran said it was too premature to consider any confidence vote in Mr Cunliffe.
