Crossbench Senator Bob Day has flagged plans for a private senators bill to revive a proposal for changes to the Racial Discrimination Act.

The Government this week dumped plans to lift the ban on offending, insulting or humiliating people on racial grounds.

Prime Minister Tony Abbott on Tuesday said he made a “leadership call” to abandon changes to section 18C of the Racial Discrimination Act as they were a “needless complication” in the Government’s relationship with the Australian Muslim community.

Mr Abbott insisted plans to change the laws are “gone”.

But Senator Day says he will try to revive the proposal when Parliament resumes later this month, because he says free speech should be protected.

The Family First senator says several Government senators and crossbenchers have voiced support for the plan.

“I would think the crossbenchers would be in favour of free speech and therefore it will be basically up to the Government to support my bill or not,” he said.

He says he will not use the plan as a bargaining chip during budget negotiations.

“I think there’s enough ammunition and argument on both these things on the budget and budget measures,” he said.

The Government’s leader in the Senate, Eric Abetz, says he is not in favour of the plan and does not think any of his Liberal colleagues will back the plan.

“I haven’t spoken to Senator Day about that suggestion but what Senator Day will do he will do, and then the Senate will come to a resolution on it in due course,” he said.

Senator Abetz says the Government has made it clear what its stance is.

“The Government’s policy has been announced by the Prime Minister and the Attorney-General that we won’t be pursing changes to the Racial Discrimination Act and that is our policy position,” he said.

“My view is the Cabinet view – that it is the wise and right thing to do, not to proceed with the proposed amendments.”