"I have indicated that to a number of parties and am going to take 24 hours and take soundings about whether there needs to be a further, forensic examination as to the source of the document which was used last night," Mallard said.
"It doesn't reflect well on the organisation as a whole, but I prefer to wait for 24 hours now before making any further comment."
Deputy Prime Minister Winston Peters was clear where he thought the leak had come from, saying that of the 56 members of the National Party caucus, 55 of them were suspect.
"They're the ones who would know, not us. We never see that information, nor any other party. No party is getting any other party's information on that matter," he told reporters.
"It just shows you that the happy family that they portray themselves [as] is not quite true."
Bridges stopped short of blaming the Government directly but said they were looking for distractions from their own problems.
"I think you' ve got to say the Government is looking for every distraction they can rather than focusing on the things they should be – plummeting business confidence, economy in downturn, strikes."
He was sure it was not one of his own MPs, although he did confirm that all of them did receive the information.
"It isn't National, I'm very confident about that."
He was pleased Mallard was looking into it. "It's good to see Trevor Mallard's doing an inquiry and we'll see what happens."
Prime Minister Jacinda Ardern has denied any of her MPs were involved.
"We've sought assurances from Ministerial Services who manage this information, that none of the opposition's numbers were shared with anyone but them and they've given us that assurance."
Ardern said she could categorically rule out anyone in Labour having access to the information, including the whips.
"The only groups, as I understand, who will have had access are the opposition themselves and the Speaker," she told reporters.
Bridges has defended the amount of money spent on his accommodation and travel, saying he was getting out and understanding the concerns of regional New Zealand.
Earlier, Ardern said that when she saw her expenses after first becoming party leader, she was surprised how high the figure for surface travel was.
"I remember wanting to change my behaviour as a result of that. These numbers, sometimes, when you think you're just out doing your job you suddenly receive an expense and some of the figures can be extraordinary. It certainly threw me the first time that happened," she told Newstalk ZB.
Ardern's surface travel for the first quarter, which included her time as opposition leader, totalled $82,795.
