The controversial backbencher continues to cause headaches for the government with rampant posts about unproven virus treatments on his Facebook page, which has more than 90,000 followers.

Prime Minister Scott Morrison and his senior cabinet colleagues have refused to condemn Mr Kelly directly despite Labor's demands he be pulled into line.

Opposition health spokesman Mark Butler attempted to censure Mr Kelly in the opening minutes of parliament for the year but the government shut him down.

"Craig Kelly is a dangerous menace and a threat to the nation's COVID response. It's beyond time that the prime minister developed the backbone to pull him into line," Mr Butler told reporters.

Despite growing pressure, Mr Kelly used Tuesday's coalition joint partyroom meeting to defend his right to post about treatment options.

In a perceived rebuke, another Liberal MP stressed the importance of everyone standing together in encouraging people to receive vaccines.

Mr Butler also took aim at Mr Kelly for appearing on conspiracy theorist chef Pete Evans' podcast.

"This really has reached peak stupid," the Labor frontbencher said.

The prime minister says Mr Kelly is not his doctor but believes he is doing a great job as a local member.

But his days as an MP could be limited with widespread speculation he will face a preselection challenge or a strong independent campaign.

Government Senate leader Simon Birmingham called on MPs to source all medical information from officials.

"Whether you're a member of the public, a member of the media, or a member of parliament - everyone should rely upon and promote the advice of the medical experts in their fields," he told ABC radio.

"Particularly when it comes to vaccines and the management of the pandemic."

Senator Birmingham said the government could not control everything MPs say in a democracy.

Labor leader Anthony Albanese said the Liberal MP's actions were undermining the vaccination effort and endangering people's health.

"Craig Kelly is not doing a fantastic job. Craig Kelly is doing dangerous job," he told reporters.

Nationals MP Barnaby Joyce said it was up to voters in Mr Kelly's electorate to judge his statements.

"Craig is not a doctor and if you're going to take medical advice from Craig, well you might as well take medical advice from me," he told Sky News.

"Brush your teeth with a black toothbrush - it works better. You know, why?"

Australians are expected to start receiving jabs at the end of this month despite ongoing supply issues across Europe.

Mr Morrison said the program remained on track with the first shipment of the Pfizer vaccine expected in coming weeks.

"But there are often disruptions to this," he told reporters.

"At the moment we are not expecting that."

There were no new cases of local coronavirus transmission nationwide on Tuesday, with WA recording a second-straight zero infection day despite a hotel quarantine breach.

Australian Associated Press