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The person who complained to the police about former Government minister Richard Worth is an Auckland businesswoman, and her allegation is of a sexual nature.

The Herald has learned the woman approached a National MP's office "to update the PM" after going to the police two weeks ago.

A friend of the woman said last night that she was distressed but pleased police were investigating.

"She has faith in the police process and trust in the Prime Minister that nobody is above the law," the friend said.

The Herald has agreed not to reveal the identity of the woman, the friend, or her associates.

The friend said the Korean woman told him "she had reported to the police alleging inappropriate behaviour by a minister towards her".

The friend, who said he knew several MPs, including Prime Minister John Key, advised her to take the matter to the Government, and helped her to do so.

The Herald was told the alleged incident took place in Wellington, but the friend refused to confirm this last night, saying it was a matter for the police investigation.

Also last night, Labour leader Phil Goff revealed that he approached Mr Key a month ago with a complaint about "inappropriate" behaviour by Dr Worth towards a woman.

"It was offers of political positions [on boards] with the underlying sense that Dr Worth was interested in the woman, shall I say, romantically," Mr Goff said.

Dr Worth resigned yesterday as Internal Affairs Minister, saying only that he was quitting for "personal reasons".

And Mr Key would not disclose any details, saying that to do so could "contaminate" the police investigation.

He said he spoke to Dr Worth on Tuesday night about the Auckland woman's complaint, and would have sacked him had he not resigned.

"His conduct does not befit a minister, and I will not have him in my Cabinet," Mr Key said.

Of the allegations raised by Mr Goff, the Prime Minister said: "The assurance I had was that they were not correct. I had no reason to disbelieve that."

Mr Goff said the woman complainant in the case he took to Mr Key was "credible".

She was a member of the Labour Party in Auckland, but Mr Goff was certain she had not been politically motivated.

She had been offered a couple of places on boards, and there was supporting email traffic.

"I felt that the allegations indicated totally inappropriate behaviour," he said.

Mr Key's chief of staff later contacted his office to say that Dr Worth had denied what was being alleged, but had been told that such behaviour would be unacceptable.

Yesterday, the police issued a statement saying they were investigating a member of Parliament after a complaint made in Auckland two weeks ago about an "alleged incident".

Mr Key said his office was contacted by a third party on Tuesday last week, two days before the Budget.

A member of his staff had investigated, and Tuesday night this week was the first time he [the PM] had spoken to Dr Worth about it.

"I think I acted as fast as I could," he said. "People are entitled to a degree of natural justice ... It took some time to get all the information that was required."

Mr Key said Dr Worth should use the two weeks of leave he started yesterday to consult family and friends on his future as a member of Parliament.

Dr Worth is a list MP who lives in Epsom. If he resigned from Parliament, he would be replaced by the next person on the National Party list, Devonport dentist Cam Calder.

Dr Worth entered Parliament in 1999 as a high-flying lawyer hoping to eventually become Attorney-General or Speaker. He had to make do last year with the post of Internal Affairs Minister outside Cabinet.

He has had a long involvement with the Korean community and has been chairman of the Korean-New Zealand business council.

The last sitting National minister investigated by police for behaving badly was Customs Minister Keith Allen in 1984.

Mr Allen claimed he had been attacked by three men while walking home from Parliament, and repeatedly denied that he had been drunk.

But police investigations revealed he had been drinking, and found no evidence supporting his report on the assault.