Australia's health department will no longer advertise on Facebook, it has announced, the latest escalation of the government's feud with the social media giant, which continues to block news content from its platform in the country.

The freeze comes as Australia begins to promote its newly launched Covid-19 vaccination rollout with a nearly US$20 million public information blitz aimed at boosting uptake and countering a flood of anti-vaccine conspiracy theories.

Health Minister Greg Hunt said on Sunday his department would still pay to promote the vaccine campaign, just not on Facebook.

"All of our funds will be used," said Hunt. "We will continue to post on that particular channel, we just won't be boosting." 

Australia's government is locked in an acrimonious dispute with Facebook over a law that would force digital platforms to compensate media outlets for online content.

Facebook strongly objects to the proposed legislation, and in retaliation on Thursday blocked virtually all Australian news on its platform.

Posts by several emergency services were briefly also caught in the blackout, sparking outcry.

The law is expected to be finalised in parliament this week and Facebook is believed to still be in talks with Australian media companies and the government to find a last-minute solution.

Facebook's dramatic response contrasted with that of Google, which has inked deals with several media firms, including Rupert Murdoch's News Corp and the Guardian.

While Australians remained unable to share news articles or view media groups' Facebook pages, the country began its vaccination drive on Sunday.

Jane Malysiak, an aged care resident and WWII survivor in her 80s, was first in line.

The prime minister and other top officials were also among a small group receiving the first jabs, before the programme expands this week to cover frontline health care workers and other officials.