Labour leader Andrew Little said the Prime Minister's tone had changed.
"There may well be now a rapidly changing position, which is because they discovered that, actually, most New Zealanders don't like this, and don't like us to be party to this."
Talk of the IRD investigating Kiwis was something of a distraction, he said, when the real issue was the use of the trusts by foreigners to avoid tax.
Labour wants the foreign trust industry shut down, but Mr Key called that a "knee-jerk" reaction.
Following the first release of details from the papers last month, the Government began a review of the disclosure rules for NZ's foreign trusts. Opposition parties have criticised the review's narrow focus.
An article in the Australian Financial Review on Friday shed new light on the number of foreign investors who had moved their cash and assets into tax-free New Zealand-based trusts, and the way these investors were able to minimise their tax.
It also said Auckland-based lawyer Ken Whitney, whose clients include Mr Key, had written a reference for Auckland law firm Cone Marshall to get accreditation with Mossack Fonseca in 2009.
After the release of the papers, Mr Key said Mr Whitney had assured him he had not had any dealings with Mossack Fonseca.
Yesterday the Prime Minister said the reference did not contradict that: "People give references all of the time."