New Zealand First members including leader Winston Peters have refused to comment on whether deputy leader Tracey Martin faced a challenge for her position.

Ron Mark was rumoured to be making a bid for the party's deputy leader position, but this afternoon it was confirmed that - if any challenge was in fact made - it was unsuccessful.

Mr Peters has left it to his party members to shed some light on the situation.

He was asked repeatedly by media who his deputy leader is and whether he could confirm Ms Martin would remain in that position.

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"I cannot discuss caucus business, that's confidential. I am restricted by that. We do not discuss caucus business outside of caucus," Mr Peters said.

During question time he faced jeers of "who's deputy". Ms Martin sat in the party's deputy chair.

Afterwards, most NZ First MPs refused to comment, but Denis O'Rourke confirmed that Ms Martin remained deputy leader.

Mr Mark also said he was not the new NZ First deputy leader, but would not comment on whether he had made or planned a challenge.

A former Rodney Local Board member, Ms Martin entered Parliament after the 2011 election as number two on the NZ First list.

Her mother, Anne Martin, was elected president in October 2013 after serving as party secretary for six years, and the two are part of a five-strong panel that decides the party list.

That influence has caused tension with some in the party.

Former North Shore City mayor Andrew Williams left NZ First after being dropped altogether from the party list before last year's election.

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He had publicly complained about his demotion in the draft list from three to 13, and said Tracey Martin was threatened by him.

Mr Mark was ranked ninth on the NZ First list at the last election.

He was a list MP from the 1996 election until NZ First failed to retain any seats in Parliament in the 2008 election.

Mr Mark was elected mayor of Carterton in 2010 and retained the position in the 2013 election.