The Morrison government has for several years been seeking to change migration laws to ensure a person cannot pass the character test if they have been convicted of a "designated offence", punishable by at least two years in jail.

Anyone who fails the character test won't automatically have their visa cancelled or refused, but rather the bill provides a discretionary ground for the minister to cancel or refuse a visa.

The minister would need to consider the circumstances of an individual case.

Labor had proposed three amendments which could have seen the bill passed by parliament in late 2021.

They included the removal of retrospectivity in visa cancellations, a reduction in the risk that low-level offending could lead to the cancellation of a visa, and a review of ministerial directions, specifically with regard to the cancellation of visas held by New Zealanders.

The government offered an alternative amendment, but later pulled out of talks and referred the bill to a short, sharp inquiry - which reported on Friday.

Labor senators said in their dissenting report the party strongly supported the current powers to cancel or refuse visas on character, criminal or other grounds under migration laws.

But the bill as proposed "appears to serve political rather than practical purposes in the day-to-day functioning of Australia's border security apparatus", raising a risk of visas being cancelled for low-level offending.

"Labor believes that the present bill, like its predecessors, is unnecessary and risks infringing the rights of visa holders without increasing protection for the community."

They argued the recent case of tennis star Novak Djokovic's visa being cancelled showed the immigration minister had very broad powers.

"The saga involving Mr Djokovic has provided a timely case study of the almost-boundless power conferred to the minister under the Migration Act."

The Labor senators also called for more consultation with New Zealand.

The Greens said in a dissenting report migration laws should be amended to prevent any non-citizen who has either lived in Australia for more than 10 years, or who arrived in Australia before the age of 10, from having their visa cancelled.

"This draconian legislation continues the expansion of the minister's powers to arbitrarily detain and deport people who do not constitute a real or significant threat. It continues the ongoing erosion of rights and freedoms in Australia and reinforces the need for a Charter of Rights."

Government members of the committee said the powers were warranted to protect the community.

"Conviction of a designated offence is a serious matter, and in the interests of community safety, it is appropriate for the minister to be given discretionary powers in relation to non-citizens convicted of these offences," the report said.

Australian Associated Press