Mr Christensen has become the first government MP in the lower house not to guarantee to support coalition legislation, amid a growing backbench rebellion in the Senate over mandatory vaccination regimes in the states and territories.

"Until federal action is taken against vaccine discrimination, I will be voting according to my conscience, or abstaining from votes ... rather than just voting with the government as MPs usually do," he said in a statement.

"I intend not to be beholden to party room discipline when voting in the House of Representatives."

It comes after five government senators - Gerard Rennick, Alex Antic, Matt Canavan, Sam McMahon and Concetta Fierravanti-Wells - crossed the floor of the upper house on Monday to support a One Nation bill to end vaccine mandates, which was defeated in the Senate.

However, Mr Christensen is the first lower house member to publicly state he would withhold support, threatening the passage of coalition bills in the chamber.

Currently, the government has the support of 76 MPs out of 151, including the Speaker, in the lower house, the minimum number for an outright majority.

Should Mr Christensen cross the floor, the government would need the support of at least one crossbench MP to pass legislation.

Crossbenchers including independent Bob Katter and former coalition MP Craig Kelly have indicated they would consider abstaining from votes due to their stance on vaccine mandates.

Opposition Leader Anthony Albanese said vaccine mandates were important measures in the states and territories.

He said Scott Morrison was sending conflicting messages to different groups over the issue of mandatory vaccines, after the prime minister argued against Queensland's upcoming mandates.

"This is a prime minister who can't control his own party room, let alone capable of governing us into the future in a way that we need," Mr Albanese told ABC News.

Despite crossing the floor to vote in the Senate to support a repeal of vaccine mandates, Senator Matt Canavan said he wouldn't withhold his support from the government on all issues.

"I don't think it's the right thing to do. That kind of tactic ... would make this place more chaotic than it already is," he told Sky News.

"While I would normally vote with the government, I do reserve the right to vote against policy as my conscience dictates."

The coalition is seeking to pass critical pieces of legislation during the final sitting fortnight for the year, including its long-awaited religious freedom laws.

Mr Christensen said he would continue to support the government on supply, as well as confidence motions.

"My support is not guaranteed on bills or substantive motions," Mr Christensen said.

"When action is taken to stop vaccine discrimination, I will go back to the normal process of voting with the government."

Australian Associated Press