At a press conference in Auckland this afternoon, Mr Craig said he supported the review but would not whether he would run for the position again.
Mr Craig said that some board members felt that a leadership discussion should be held.
"I am fully supportive of the call for a review," he said.
He said he had offered to stand down as leader "to enable the board to consider the leadership role".
Mr Craig would also work with the party secretary to forgive any outstanding loans between him and the party.
Party chairman Brian Dobbs said today there "was is a desire to engage in a discussion around leadership" and he was grateful to Mr Craig for standing down to allow the board "to explore all possible leadership options going forward".
Mr Dobbs thanked Mr Craig for his contributions to the party and for his leadership in its first four years.
"He has shown outstanding commitment at advancing the cause of conservatism in New Zealand. Colin has also advised me that regardless of any board decision, he will remain an active member and supporter of the party."
Mr Craig called the press conference after reports emerged of a leadership challenge to occur at a board meeting tonight. He said there had been many rumours, "ranging from the intriguing to the ridiculous" about the meeting, which has now been postponed.
The potential leadership coup was believed to be prompted by a recent appearance by Mr Craig on TV3's late night show Newsworthy, where he was interviewed in a sauna with journalist David Farrier.
TV3 quoted an insider saying that it was the "last straw" and it was "crazy Colin all over again".
Mr Craig said today he did not regret the TV appearance, but that he was "big enough" to see that other members of his party had different perspectives on it.
Some members are believed to want former Conservative candidate Garth McVicar to take over the leadership role. Mr McVicar has said he has no interest in replacing Mr Craig.
After failing to get elected in the Napier seat, Mr McVicar returned to his job at the hardline law and order reform group the Sensible Sentencing Trust.
Rumours of a leadership spill arose in March when Mr McVicar was invited to a board meeting, despite leaving the party after the general election in September 2014. Mr McVicar turned down the invitation to attend the meeting.
Mr Craig, a wealthy property manager, has invested close to $4 million in the party since founding it in 2011.
But despite that investment, and a high profile election campaign including well-known candidates Christine Ranking and Mr McVicar, the party won no seats in September's general election.
Mr Craig said that if the party decided to elect a new leader, he was likely to remain a member and continue investing his money in the Conservatives.
