The Labour Party is furious about a letter claiming there is a plot to overthrow leader Phil Goff and is trying to hunt down the author.

The anonymous letter, sent to several media organisations' political editors, was in an old airmail envelope with Office of Minister of Finance, NEW ZEALAND printed on it.

The single-page letter said union-based MPs would challenge Mr Goff on Tuesday about a government plan to allow workers to cash in their fourth week of holiday.

The measure was one of a number of controversial labour changes the Government announced last week.

Mr Goff is reported to have told a radio station that he didn't have huge objections to the fourth week being cashed up as long as workers arrived freely at their decisions and were not pressured.

National MPs frequently mock Mr Goff's leadership and call him "Fill-in", saying he is just keeping the seat warm for the next leader.

Labour deputy leader Annette King was visibly angry when questioned by reporters.

"It's a piece of malicious mischief," she said.

The party did not know who the letter was from.

"I don't know but, as you know, I am a former minister of police and let's say we are following some leads... I would hope we would (trace them). It's a piece of malicious fabrication."

She would not speculate on whether it could be a sitting MP or a former staffer.

The letter said the issue had bought to a head "growing discontent" within the Caucus about Mr Goff's leadership and poor polling.

"David Cunliffe has a big smile on his face and many in the caucus now expect a move against Goff and King before the election."

Mr Cunliffe said the letter was "complete rubbish and like my colleagues I am cross about it. Look at my face. That's (the smile claim is) rubbish too."

He ruled out a leadership attempt before next year's election and said Mr Goff had his "100 per cent" backing.

The letter also said George Hawkins would be challenged for his Manurewa electorate seat by a member of the Engineering, Printing and Manufacturing Union (EPMU) before nominations closed on September 1.

"George is threatening a by-election and since the party is broke, there is panic in the ranks over this prospect."

Mr Hawkins was cagey about his plans.

"I've read all sorts of rumours," he said.

Asked if he had threatened a by-election he said; "Come see me New Year's Day when it's a lean news days and I will tell you".

He would not confirm if he knew whether there was an EPMU contender.

"Lots of people always want to stand against me. None of them have succeeded."

Finance Minister Bill English was asked about the envelope the letter was sent in. It was not current stationery.

He said the letter showed the strains of being in opposition. He said he believed the letter was internal rather than trouble making from National or another party.

"I'd be very surprised. Labour are starting to show the pressures of opposition. They'll start attacking their leader and being internally split. I think it will get pretty ugly."