"They're trying to get to the bottom of some claims that have been made, and doing it quickly so we can get on with holding a successful America's Cup," Twyford told reporters today.
"We all want to get on with organising a successful America's Cup in the summer. I don't think it does jeopardise the Cup."
Asked if the allegations tarnished the event, Twyford said: "The America's Cup is no stranger to drama, but in this case we'd like to get it sorted out as quickly as possible."
He would not be drawn on any details of the issue or the contractors involved.
"It's a dispute. It's an argument. We want to get it all sorted out so they can get back to work."
One of Team NZ's rival challengers has denied any involvement in the scandal.
Sir Ben Ainslie, an Olympic superstar, has told NZME that his America's Cup challenging team are in the dark over the allegations.
INEOS Team UK skipper Ainslie told NZME they haven't received anything and CEO Grant Simmer says they are certainly not involved.
"There's no comment from us as we've got no insight into what's happened," said Ainslie, who turned around Oracle's fortunes as they scored their famous comeback win over Team NZ in San Francisco seven years ago.
Fellow European syndicate and challenger of record Luna Rossa could not be reached for comment.
Earlier today Prime Minister Jacinda Ardern said she wasn't concerned that the spying allegations that have rocked Team New Zealand will affect the country's hosting of the 2021 America's Cup.
"We're all committed to making sure we do a fantastic job of hosting the America's Cup. That's where everyone's efforts are going in to," she said.
"Obviously there are some issues that are being looked into presently by MBIE, but I don't want to be drawn too much on them because at the moment it's speculative."
Dalton, speaking on the Mike Hosking Breakfast this morning, would not say how many people they thought might behind leak allegations, but confirmed that they were not dealing with a single person.
"It's hard to believe it would be a plant. But, you know, when you get inside an organisation like ours and you've got pretty much free access, you know, it can do things to people."