Asked about his likeability, Mr Cunliffe said he had "lots of friends around the caucus''.
"I think there might have been a little bit of spiking of the guns by someone, I'm not accusing my colleagues here, but people put tags around for their own reasons and I'm not going to responding in kind to that.
"I know that I've got lots of good relationships and I've built a really, really strong team in my own electorate, and I think that speaks for itself.''
Mr Cunliffe said they were all "pretty good mates'' and after the selection process everyone would need to bind together.
Mr Parker said he would bring integrity and substance to the role.
"We fought and won victories for the working class in the past, but today to be relevant we've got to change to become the party of today's working people, and not be too stuck in the old structures of the past.''
Mr Parker said he'd shown ability as a lawyer, businessman and politician.
"I'm not John Key, I don't want to be John Key. I bring different values to the job and I will shine if I'm given the opportunity.
"John Key is a popular man but he's not delivering for ordinary New Zealanders, we've seen the gap between the rich and the poor grow. If I became the leader of the Labour Party, I would present a vision that is appealing to the ordinary New Zealander, to the working classes.''
Mr Parker said there was no shame in running, winning or losing.
"I think all of us are mature enough to, in the end, put the interests of the Labour Party ahead of our personal interests.''
Mr Shearer said being new to Parliament was an opportunity and he could bring a fresh look.
He came into the role having run large teams with the United Nations in incredibly difficult circumstances, including in Iraq, Palestine and Somalia.
"These are places where you've got to build large teams together, have them highly focussed, getting on with the job and working together to get a result. And I think I can use those sorts of skills and that sort of background with a fresh look to the Labour Party.''
Mr Shearer said people acknowledged he had a new perspective that was different from the past.
"I wasn't in the Helen Clark government, they did some wonderful things. But I think that the Labour Party - like they did under David Lange, like they did under Helen Clark _ needs to reform, it needs to be refreshed and it needs to reconnect with New Zealanders.
"I don't believe, and the election results showed that, that we are the inspiration for New Zealanders. They did not look at us as being their inspiration in taking New Zealand forward, and we need to rebuild that and make it foremost in their minds.''
Mr Shearer said over the next few days, the caucus and wider party had to articulate a new vision for Labour.
