Mr Parker refused to comment on the leaks or speculation about the leadership camps, saying he did not talk about internal matters.
Mr Goff said he had full confidence in his front bench - the last MP to breach caucus confidentiality was Chris Carter, who was expelled.
"I'm confident in the integrity of my members, both in the front bench and in the Labour Party caucus."
However, it is understood the need for discipline was strongly reinforced at the caucus meeting.
Clearly frustrated by the ongoing speculation, Mr Goff said it was clear he would stay as the leader. "It's about time people stopped flogging that dead horse and just accepted the fact."
Asked about the poll result, Mr Goff said Labour was the underdog but would pull through once voters began to focus on policies.
"We need to focus the electorate on those issues once the World Cup is behind us and the election campaign is under way. I'm quite confident that Labour has policies that can win the support of the majority of New Zealanders."
Mr Goff said he was comfortable with comments made over the weekend by MP Shane Jones. Mr Jones had hit out at the source of the leaks and manoeuvring for leadership on TV3's The Nation, including saying Mr Cunliffe should focus on selling Labour's economic policy as he had promised. Mr Jones had also said his own leadership ambitions were currently at "a low ebb" and any change in that would depend how he fared in the Tamaki Makaurau electorate.
The day did have its moments of humour. Midway through Trevor Mallard's attempts to dismiss talk of leaks, the quacking ringtone of his cellphone erupted. When asked who was leaking, Mr Mallard pointed back down the corridor in the general direction of Shane Jones' office and said "I think you could go and check down there as to who's leaking. You know where leaks occur, don't you?"
It was not until after Mr Jones was asked about it by media later that Mr Mallard realised he was misinterpreted and visited the Press Gallery to point out that he had in fact been talking about "the dunny" just opposite Mr Jones' office. "That's where leaks happen."