Prime Minister Tony Abbott is facing a rebellion in the Senate, with up to half a dozen of his own senators indicating they could cross the floor in favour of changing race hate laws.

In a sign of Mr Abbott's diminishing authority, West Australian senator Chris Back and Queensland Liberal National Party senator Ian Macdonald have told Fairfax Media they will vote in favour of a bill designed to water down the Racial Discrimination Act.

South Australian senator Sean Edwards has given a strong indication he could join them, arguing the act in its current form suppresses free speech.

Mr Abbott pledged before the 2013 election to repeal section 18C of the act after conservative commentator Andrew Bolt was found to have breached the act for his articles about "fair-skinned" Aboriginal people. But the Prime Minister abandoned his pledge last year after a fierce backlash from religious leaders and many Liberal MPs.