Speaking in Sydney on Tuesday, Prime Minister Scott Morrison has also described being banned from entering Russia as a "badge of honour".

Foreign Minister Marise Payne said chemical attacks in the beseiged city of Mariupol would constitute a "wholesale breach of international law".

Far-right paramilitary group the Azov Battalion, which has been folded into Ukraine's official army, has accused Russian troops of using an unidentified chemical substance in the holdout city, leaving victims struggling for air.

Ukrainian President Volodymyr Zelenskyy was yet to confirm the attack, but warned Moscow may be prepared to use chemical weapons unless sanctions were tightened.

The Pentagon and Downing Street were working to verify the reports, which Ms Payne described as "extremely concerning".

"If they are confirmed, that will be a further wholesale breach of international law," she said.

"[It will be] a further indication of President Putin and Russia's absolute violation of every single value, and of the rules-based global order which has stood us in such good stead for so many decades now.

"Australia will be working with our counterparts to determine the veracity of these reports, and we'll have more to say on that."

Russia's advance has been frustrated by stronger-than-expected resistance from Ukrainian forces, leading Moscow to shift its focus to the country's east.

Experts have warned Russian President Vladimir Putin was likely to escalate his tactics to break the deadlock.

Human Rights Watch found the Syrian government, supported by Moscow, used chemical weapons to attack its own civilians during the country's bloody civil war.

Moscow last week retaliated for retaliated to "unfriendly sanctions" and Australian military support for Ukraine by banning more than 200 politicians - including Mr Morrison and Labor leader Anthony Albanese - from entering Russia.

But the Prime Minister, whose government sent 20 Bushmaster armoured vehicles to Ukraine this month, insisted Australia would not be deterred.

"I have copped a lot of criticism, not just from Russia, but from countries in our own region," he said.

"I'm happy to wear that as a badge of honour for standing up for Australians. Australians know I'm not a pushover."

Two members of the Azov Battalion, which has been accused of war crimes in eastern Ukraine, joined President Zelenskyy for a video address to Greek parliament, leading some MPs to stage a walk-out.

Former Defence secretary Dennis Richardson last month conceded Australian weapons could end up in the hands of extremists in Ukraine, but said the priority was ridding the country of Russian troops.

"Bad things might happen down the track as a result of the arms that are now flowing into Ukraine ... [but] that is something that will need to be addressed if and when the time comes," he said.

"If there is a risk that down the track that arms might fall into the wrong hands, then so be it."