Labor is demanding Scott Morrison pull a rebel Liberal MP into line for undermining the coronavirus vaccine rollout by spreading misinformation.
Craig Kelly continues to cause headaches for the coalition with rampant posts about unproven virus treatments on his Facebook page, which has more than 90,000 followers.
Labor's 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 on Tuesday.
Prime Minister Scott Morrison says Mr Kelly is not his doctor but praises the Sydney MP for doing a great job as a local member.
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.
No senior government minister has condemned Mr Kelly directly.
Labor leader Anthony Albanese said the Sydney-based Liberal'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.
"Scott Morrison has a member of his caucus who is undermining the health response to this pandemic and yet he won't even say anything to distance himself from Craig Kelly."
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."
