Tensions emerged after it was disclosed that Mr Blair had been confronted with criticism at a series of meetings with backbenchers to "clear the air" over the direction in which he is taking the party.
Reports that the Labour leader was confronted by a "mutiny" were strongly denied by people from both sides of the party who were there. However there appears to be internal policy strains, particularly over the threat to cut child benefit for 16- to18-year-olds.
Dismissing the rifts as "tittle tattle", Mr Cunningham said on BBC1 television's Breakfast with Frost: "I know they know how challenging the task is and how important it is for them and everyone else in Labour's team to work together to maximise the opportunities for victory."
Last night one hard-left Labour MP said: "There is not a crisis at all. They were friendly meetings. There was not a mutiny. Blair was very relaxed.
"They were cathartic because we had had a good moan, but it was likely that it would influence nothing at all in the style and content of the leadership's policy drive."
Gordon Brown, the shadow Chancellor, is being blamed behind the scenes for failing to consult colleagues about major policy announcements, including his desire to cut child benefit for 16- to18-year-olds in full- time education.
Some of the MPs, including loyalists, complained that they were being taken for granted. David Hanson, parliamentary private secretary to John Prescott, the deputy leader, is reported to have told Mr Blair: "I feel like a sponge soaking up criticism on policies I only hear of on the radio."
London MP Tony Banks said: "People want help. If we don't deliver I will need a tin hat when I walk in the streets."
Ken Livingstone defended Clare Short, the shadow Transport Secretary, for appearing to support a higher rate of tax. Denis MacShane, MP for Rotherham, and a moderniser, said it would be difficult to tell a teacher couple earning around pounds 70,000 together that they should pay more in tax.
Mr Blair appeared at the meeting, one of a series about a fortnight ago, without his press secretary, Alastair Campbell, or any other Shadow Cabinet colleagues. A polling expert told the group of MPs - drawn from all sides of the party - that private polling evidence showed the Tories were mistrusted, but that the electorate was not certain it could trust the Labour Party. "The message was clear - that we should not disrupt things if we wanted to win the election," said one Labour MP.
"Tony talked about the importance of discipline. We explained to him he didn't understand just how disciplined the party was at the moment. We have never known the party more self-controlled in the sense of knowing we have to win the next election, and we are willing to button our lips to do so."
Others present included Allan Rodgers, Ken Eastham, Gerry Bermingham, Mildred Gordon, Alan Simpson, Terry Lewis, and John Austin-Walker.
Mr Hanson said last night: "The meeting I was at was not an angry confrontation but a sharing of views and a very positive discussion between the leader and MPs from all wings of the party. There was no anger. There was no outrage. The meeting was very positive."
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