Hundreds of people who have arrived in Australia after fleeing Gaza have applied for asylum, as they face expiring or expired short-term visitor visas. 

Last month people of "Palestinian Authority" nationality became the second largest cohort lodging protection applications onshore, after China.

At least 749 Palestinian Authority passport holders have arrived in Australia and claimed asylum since October, when the federal government began granting tourist visas to people fleeing Gaza.

Australian Palestinian Advocacy Network president Nasser Mashni said people were applying for protection as a desperate measure.

"No Palestinian wants to leave Palestine. In fact, most if not all Palestinians want to go home. These Palestinians that have fled Gaza are desperate, and it behooves a country like Australia to afford them that opportunity and create pathways as to not contribute further to the angst and pain they're suffering already," Mr Mashni said.

"There's nowhere for them to go. They've lost everything and surely as human beings we should be offering them security and safety."

The federal government is considering a longer-term solution for the cohort of Palestinians in Australia.

Shadow Home Affairs Minister James Paterson said the government had "improperly" granted tourist visas to people fleeing Gaza, because it knew people granted those visas had no intention of returning at their expiry.

"They should have been taken to a third country where they could be removed from danger but assessed carefully, as we did in Syria and Afghanistan, for security and identity and also whether they met the criteria for refugee humanitarian protection," Senator Paterson told Sky News.

Lodgement rates much higher compared to Ukrainian cohort after Russia's invasion

Unlike the Coalition's decision to offer three-year humanitarian visas to Ukrainians fleeing at the beginning of Russia's invasion, the federal government has not established a dedicated humanitarian visa for Palestinian people fleeing Gaza.

Nearly 11,400 Ukrainians have arrived on "temporary humanitarian stays" since the former Morrison government made the offer on March 20, 2022, just a month after the war in Ukraine began.

In the same time, at least 952 Ukrainians have made onshore applications for permanent protection, about 8 per cent of that cohort (though not all who applied were necessarily people on temporary humanitarian stays).

Meanwhile, about half the rate of Palestinian people who have arrived since October have sought asylum, with the only other option available when their tourist visas expire being to be placed on a bridging visa.

Government and opposition trade blows over ASIO boss remarks

The Coalition has been applying pressure on the government's processes around allowing Palestinian people to enter Australia for several weeks, which became inflamed after remarks made by Australian Security Intelligence Organisation boss Mike Burgess on ABC Insiders.

Asked whether it was a problem if Palestinians seeking to enter Australia had expressed support for Hamas, Mr Burgess said "if it's just rhetorical support and they don't have an ideology or support for violent extremism ideology, then that's not a problem".

Overnight, Mr Burgess said those comments had been misrepresented.

"I said that if you support a Palestinian homeland that may not discount you [from entering Australia] because that by itself is not a problem," Mr Burgess told 7.30.

Opposition Leader Peter Dutton said he welcomed the "clarification", but repeated his accusation the prime minister had misled parliament by suggesting ASIO had vetted each individual when they had not.

"I think he's put Mr Burgess in a difficult position, I think frankly he should be apologising to the ASIO boss," Mr Dutton said.

Mr Albanese said the "only person who had been critical" of the ASIO boss was Mr Dutton, suggesting their "attempts to dissect" his words were a challenge of Mr Burgess.

Senator Paterson challenged why after a month of debate, the federal government had not come forward to clarify the distinction between support for Hamas and support for Palestinian statehood.

"It's up to the government to say, which the prime minister has been unable to, that supporting a terrorist organisation violates the character provisions of the Migration Act, and we will not grant you a visa if you support Hamas," Senator Paterson told Sky News.

"None of that is a matter for Mike Burgess, none of that is a matter for ASIO. They don't administer that act, the government does."