Protests against the planned legislation, which would permanently ban asylum seekers who arrive by boat from settling in the country, come as far right groups demonstrate against moves to rehouse 120 refugees.
A United Nations official said Australia would probably be in breach of the Refugee Convention if it enacts a proposal for a permanent visa-ban on asylum seekers who attempted to reach the country by boat, Fairfax Media reported on Saturday.
Prime Minister Malcolm Turnbull proposed last Sunday that asylum seekers sent to the county's offshore processing centres would be prevented from applying for any visa to Australia, even if they had been classified as refugees or resettled in another country.
The United Nations High Commission for Refugees' regional representative, Thomas Albrecht, said such a move would likely breach the convention's article prohibiting the punishment of those seeking asylum.
The proposed permanent visa-ban would be applied to anyone transferred to a regional processing centre after 2013, including some 1,400 people currently held offshore.
"While solutions for refugees currently on Nauru and Papua New Guinea are critical, third-country settlement for them would not alter Australia's fundamental obligations to provide asylum to those who need and seek its protection, including by sea," Albrecht said, according to Fairfax Media.
Thousands protest against proposed ban
Also on Saturday, protesters in Melbourne, Sydney, Tasmania and dozens of regional centres called for the closure of offshore processing camps, which have been heavily condemned by the United Nations refugee agency (UNHCR), and for asylum seekers and refugees to be brought to the mainland.
Organised by the groups Refugee Action Coalition, the Refugee Action Collective (RAC) and Doctors for Refugees, the rallies focused specifically on the proposed ban.
Chris Breen, spokesperson for the RAC, which organised the 3000-strong rally that took place in Melbourne, issued a statement on Saturday condemning the government's recently announced intentions.
"The proposed legislation is a discriminatory punishment for refugees that would permanently split families. If carried through it would result in hundreds of deportations from Australia to indefinite offshore detention."
Breen described the government's refugee policy as "callous, discriminatory, dysfunctional and increasingly desperate."
Australian Greens leader Senator Richard Di Natale addressed the crowd.
"Today must mark the end of this race to the bottom," he shouted into the microphone above loud cheers.
"We're here today to take a stand against the vicious racism that lies at the heart of this policy directed towards innocent people seeking asylum."
Australian far-right groups demonstrate against plan to rehouse refugees
Several hundred people rallied in the suburbs of Melbourne on Saturday after a proposal to house 120 asylum seekers locally drew protests from far-right anti-Islam groups as well as counter protests.
Dozens of people belonging to the anti-Islam groups rallied against the proposal, which involves housing the refugees from Syria and Iraq at a housing facility for elderly citizens in the Melbourne suburb of Eltham.
"They (the elderly citizens) are a bit concerned about it but they will just wait and see," John Conroy, a resident of the aged-care facility said.
A heavy police presence separated the group from more than 100 people rallying in favour of the proposal. Previous protests between anti-immigration and pro-immigration groups have led to violent clashes.
Last year the government announced a one-off intake of 12,000 refugees fleeing the conflict in Iraq and Syria, saying that ethnic minorities from those countries would be given priority.
Far-right political parties are on the rise in Australia, with the controversial One Nation party surprising many by winning four Senate seats at the country's national elections in July.