Former Kiwi cricketers Low Vincent, Chris Cairns and Daryl Tuffey were earlier reported to have been investigated by the International Cricket Council as part of a match-fixing probe.
"We need to let the investigation by the ICC run its course," the Crains said in a brief statement to Fairfax Media, adding it was the only comment he was prepared to make.
Cairns was working for Sky TV as a commentator in Dunedin where New Zealand are playing the West Indies, but left the ground early in the afternoon.
A Sky TV spokesman said Cairns "elected to stop commentating on the current Test match and come back to Auckland to be with his family".
"Sky will be talking to him over the coming days."
All-rounder Cairns - son of bowler Lance - is one of New Zealand's most decorated players with 279 international appearances to his name.
His 218 Test wickets places him fourth on New Zealand's all-time wicket-taking list while his 3320 Test runs puts him in the top 10 in Test runs scored.
He is also in the Black Caps' top five for both ODI wickets and runs.
Cairns last year won 90,000 pounds ($147,000) in a libel action against former Indian Premier League chairman Lalit Modi in London.
He had sued over an "unequivocal allegation" of involvement in match-fixing made on Modi's Twitter account in January 2010.
Former New Zealand international Lou Vincent confirmed he was "cooperating" with the ICC.
"This investigation is bound by a number of rules and regulations that mean I am unable to make any further public comment," he said in a statement.
Another player linked to the investigation is now believed to be living in Australia.
Both the ICC and New Zealand Cricket have refused to identify the three players under investigation, other than saying they are former internationals and that no charges have been laid.
"It is alleged that a small number of former New Zealand cricketers had engaged in fixing activity," the ICC said in a statement after New Zealand media reports stated that the probe was targeting three players.
NZC chief executive David White said earlier he knew the names of the players but would not elaborate, other than saying that current members of the New Zealand team were not involved.
"We have been aware for a number of months," White said.
"We are shocked and surprised and support the ICC investigation as corruption has no place in our sport."
The ICC's anti-corruption unit has spent four months in New Zealand investigating match and spot fixing, which The New Zealand Herald said took place in more than one country.
Details of the investigation became public in the middle of the first Test between New Zealand and the West Indies in Dunedin, although White said no current players were involved.
The ICC probe did not involve any games played in New Zealand nor any under NZC jurisdiction, he added.
White said the ICC was keeping New Zealand officials informed of progress in their investigation but he had no idea how long it would take to complete.
The ICC statement said as the investigation was ongoing and no-one had been charged with any offence, it would be making no further comment.
"The ICC and all of its members maintain a zero-tolerance attitude towards corruption in the sport, and the Anti-Corruption and Security Unit will continue to collaborate with relevant individuals in order to complete its investigation process," it said.
Former New Zealand bowler Iain O'Brien indicated it was likely New Zealanders had been involved in match fixing.
"If you're surprised that Kiwis are involved in match fixing, you're sadly naive," he tweeted after details of the investigation emerged.
"I highly doubt any players are 100 percent clean."
Earlier this year, NZC dismissed an English newspaper report quoting an Indian bookmaker saying he had been involved in match-fixing with New Zealand players.
"We have complete confidence that the claims made are baseless and have no credibility," White said in a statement at the time.
"The sources are not credible and the accusations are unsubstantiated, making them irresponsible, damaging and untrue."