Stephanie Foster and senior departmental officials appeared before a last-minute Senate committee hearing on Tuesday evening, detailing legislation which was rushed through the lower house earlier in the day.

The proposed legislation would give the immigration minister special powers to order non-citizens, who had exhausted all paths to stay in Australia, to take steps to facilitate their own removal.

This would include applying for passports and other steps to attain travel documentation.

Failure to comply, without a reasonable excuse, would constitute a criminal offence with a mandatory minimum of one year in prison, and a maximum sentence of five years.

The Albanese government hopes to pass the legislation through Parliament by the end of Wednesday, the last sitting day until May.

It has said this is because it is a gap in the migration system, which should be plugged immediately.

However, Coalition and crossbench senators questioned whether the legislation was a response to a case before the High Court, known as ASF17.

In a separate case last year, the High Court ruled it unlawful to detain non-citizens when there was no prospect of removing them from Australia in the foreseeable future.

But ASF17 could affect those who have not cooperated with deportation efforts, and who have therefore remained in detention.

"It does not respond to the points of law that are being tested in ASF17," said Clare Sharp, the department's general counsel.

"It does deal with the same cohort of people that will be affected by the outcome in ASF17."

Officials would not say whether the government intended to use the legislation in response to the High Court ruling.

Senators grew frustrated as they questioned hesitant bureaucrats on the urgency of the legislation.

"If the Commonwealth were to lose the case, would this legislation give the government other options for dealing with that cohort," Liberal senator Paterson asked.

"For example, if they continue to refuse to co-operate, it would now be an offence which they could be charged and incarcerated for?"

"Our view would be that these are powers that should exist in the Migration Strategy regardless of any litigation," said immigration policy group manager, Tara Cavanagh.

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But Ms Foster did state that the bill, if passed, could be used to address the cohort affected by ASF17.

"Yes, if the bill were passed, and the case were unsuccessful, it would give us an additional tool to deal with people affected by that," she told Senators.

Public servants also revealed they had advised the government of the need for the legislation in February, and that drafting instructions were issued on March 5. Drafting was concluded last Friday, they said.