The government wanted to force a vote in the Senate on Wednesday but failed when the opposition unexpectedly teamed up with the Senate crossbench to kick the legislation to an inquiry.

It will report back on May 7.

The coalition argued a two-hour, late-night hearing with officials wasn't enough to allay concerns about unintended consequences or the need for urgency.

The coalition was briefed on the laws on Tuesday morning before a vote took place in the lower house hours later, where the opposition supported the bill.

Prime Minister Anthony Albanese criticised the opposition's about-face and its call for more scrutiny.

"Everyone had time to scrutinise it," he said on Thursday.

"This is closing a loophole ... this is about people who have not been shown to have any right to be in Australia."

The coalition was inclined to support the new measures, opposition home affairs spokesman James Paterson said, but a case hadn't been made about why they needed to pass so urgently, without sufficient scrutiny.

Home Affairs Minister Clare O'Neil and department officials have been unclear whether the urgency is linked to an upcoming High Court case.

An Iranian man, known as ASF17, wants an earlier ruling, that indefinite immigration detention was illegal for those who could not be returned to a third country, to also cover detainees who refuse to co-operate with their deportation.

Labor's new laws also impose up to five years in prison on top of up to a $93,000 fine on people found to not co-operate with their deportation.

In addition, the minister would have the power to ban visa classes for countries that don't accept deportees

"I think the ASF17 case does show that it is important that we have these powers, it's not the only reason why we're doing this, though", Ms O'Neil said.

Home Affairs Department legal counsel Clare Sharp said the bill didn't respond to "the points of law being tested" in the case.

Wednesday was the last day parliament was sitting until after the court case on April 17.

Senator Paterson says if the case was made that the laws needed to be in effect before then, parliament could be reconvened.

"If there is a link, they should say so, but they have also said they are very confident about their prospects in that case," he said.

The government has been under fire from the opposition after 152 immigration detainees were released under the initial High Court decision.

Immigration Minister Andrew Giles has repeatedly said the cohort was being strictly monitored by authorities, including with ankle bracelets and curfews.

But the opposition has seized on evidence from department officials that 73 people in the cohort weren't required to wear ankle bracelets.

Some former detainees who challenged needing to wear ankle bracelets in court had them removed by the government before a decision was required.

Removing the bracelets before a court decision prevents a judge from setting a precedent to remove bracelets from others in the cohort.

A community protection board had reviewed all individual cases and determined some ankle bracelets were able to be removed, the government said.

Ms Sharp said the new laws could also result in individual cases of the 152 detainees being revisited as a new pathway for their removal could be identified through the coercive powers.

Australian Associated Press