Immigration Minister David Coleman introduced the bill to the lower house of parliament in July, saying the changes are needed to protect the community.
"This bill ensures that non-citizens who have been convicted of serious offences, and who pose a risk to the safety of the Australian community, are appropriately considered for visa refusal or cancellation," he said.
"The bill presents a very clear message to all non-citizens that the Australian community has no tolerance for foreign nationals who have been convicted of such crimes."
Jacinda Ardern has described Australia's deporting of foreign-born criminals 'corrosive'
'Strikes appropriate balance'
The Senate Standing Committees on Legal and Constitutional Affairs conducted its inquiry over two months, receiving 32 submissions and hearing from 23 individuals during a one-day public hearing.
In its final report, the committee said the bill "strikes an appropriate balance" between community safety and the rights of non-citizens who commit crimes captured under the category of "designated offences".
The category includes offences which attract a maximum term of two years or more; and also involve a physical element, such as sexual violence or possessing a weapon.
The Labor party and Greens dissented from that majority recommendation, with Labor senators finding the changes unnecessary.
The bill "has the potential to infringe the rights of visa holders without increasing protection for the wider community", Labor's dissenting report said.
Labor senators also expressed concern about the impact of Australia's relations with New Zealand, considering the number of Kiwis deported under the character test as it currently operates.
The Greens said in its dissenting remarks the government had "failed to present a case for these additional powers".
Of particular concern, the party said, was the retrospective operation of the proposed bill, applying to any non-citizen convicted of a "designated offence" at any time.
Increased ministerial discretion
Failing the character test on these grounds would not result in automatic visa refusal or cancellation, with the minister still exercising discretion on the matter.
The proposed changes signal a widening of the discretion held by the minister after changes in 2014 which allow the government to deport non-citizens sentenced to at least 12 months jail for their crime.
That change has resulted in more than 1,000 Kiwis being sent back between 2016 and 2018 - a situation which New Zealand Prime Minister Jacinda Ardern said is having a "corrosive" impact on the bilateral relationship.
Former Labor policy advisor Henry Sherrell said in his submission to the inquiry that he believed the number of people affected, particularly with "non-jail sentences", would be significant.
"It could be by a factor of five, including people who are unlikely to be an ongoing threat to the Australian community," he said in his submission.
The majority view of the committee said it was reassured by departmental advice "that the bill is compatible with human rights".
It described the government's bill as "appropriately strengthen[ing] the existing character test framework".
"The bill provides a clear and objective basis for failure of the character test that also allows for decision-makers to appropriately consider a range of matters for each non-citizen's case."
Labor said the negative impact of the changes on the bilateral relationship with New Zealand is of "profound concern".
The party has recommended that Australia adopt New Zealand's approach of not deporting people who have lived in the community for 10 years or more.
The Greens party said it shared similar concerns, particularly in scenarios when long-term residents of Australia would be separated from their family in Australia and "removed to a country where they do not speak the language; where they have spent little time [or never lived]; and where they have no familial, social or economic connections".