The Opposition has flagged on Thursday that it is now open to passing the government's migration fix to give greater ministerial powers to compel people to cooperate with authorities trying to deport them if Labor can "demonstrate genuine urgency."

This comes after a surprise move by the Coalition on Wednesday to combine with the Greens and crossbenchers to thwart the government's attempt to ram it through Parliament before a six-week break. With senators wanting better scrutiny, the legislation has been referred to a Senate inquiry which is due to report back on the next sitting day, May 7.

The Prime Minister insists "everyone" has had time to scrutinise the legislation, saying a full briefing was given to the Coalition.

"This is filling, closing a loophole which is there in the legislation, one that was there under the former government," he told reporters in the Hunter Valley.

"I found it astonishing that the Coalition had three policies. They were for it on Tuesday. They were against it on Wednesday morning and deferred it and then said maybe Parliament should come back to vote for something that they had just voted against voting for.

"So I think it's up to them to explain why they had three positions over the last two days."

The matter, reopened by a High Court ruling last year that led to the release of almost 150 people from immigration detention, has caused major headaches for the government particularly Home Affairs Minister Clare O'Neil and Immigration Minister Andrew Giles.

The Coalition has been critical of the timing of the briefing it was given, saying it was "shambolic" and "absurd" that it was given on the morning of the legislation's introduction in the House on Tuesday.

Peter Dutton outlined the opposition's issues to Sydney radio station 2GB.

"So, what we said was, 'okay, we'll allow it through the Lower House because you're telling us it relates to this court case that's coming up and it's an urgent matter, but we want to get it up to the Senate so that there can be a reference to a Senate inquiry'," he said.

"And that's where the public officials come and they can be questioned about what's in the bill, but when we got to that process, we find out that it doesn't actually relate to the court case now before the High Court, and the government's been sitting on it for a number of weeks."

Without evidence, the Opposition Leader is also claiming he "fears" that they're creating a potential pull factor in getting people back onto boats.

"So, I think the longer inquiry now will answer some of the questions that the officials and the ministers refused to answer initially, and we'll be in a better position to know whether this is going to start boats again or not," he said.

There was a spillover estimates hearing on Tuesday night with Home Affairs officials, including the secretary Stephanie Foster, that it was not satisfied with. And then there was another spillover hearing on Wednesday night.

The Opposition's James Paterson has conceded that the Coalition, in principle, will likely back the legislation and is open to bringing Parliament back early.

"If the government is able to do what it hasn't been able to do this week, which is demonstrate genuine urgency, we can bring the Parliament back."

"We will bring our members and senators back whenever required to pass this legislation.

"If the government unexpectedly loses the case, and they do explain that it's necessary to manage this cohort, we will bring the Parliament back. That's an offer that we've made to them. It's an offer which remains open. And so if there is a genuine need, of course, we'll play a responsible role in fixing this problem."

Legal experts and refugee advocates have run alarm bells over the proposed law change, calling the move draconian and unprecedented.

The Prime Minister has outlined his case for the new laws.

"To be very clear, this isn't about refugees," he said. "This is about people who have not been shown to have any right to be in Australia, be it refugees or be it family reunion status or anything or any other measures."

"My government is orderly. My government rolls out policies in an orderly way consistent with what our program was that we were elected to implement in 2022."