Senior conservative Peter Dutton says it will be “impossible” to insert additional religious protections in the cross-party same-sex marriage Bill.

Conceding defeat over proposals to amend the legislation to introduce wider religious exemptions, the Immigration Minister said Parliament was “governed by arithmetic” and conservatives had failed to win the necessary support for the changes.

His admission came after Government Leader of the House Christopher Pyne vowed to oppose “superfluous” amendments and pass the Bill authored by WA Liberal senator Dean Smith in its current form.

Liberal Lower House MPs Jason Falinski and Trent Zimmerman have also pledged their support for the Bill as it stands.

Mr Pyne argued that amendments should not be based on the “misnomer” that religious freedoms were not protected in Australia.

“I think the protections in the Bill as they stand now for religious ministers, for defence pastors, for religious institutions are quite adequate,” Mr Pyne said.

“We have other laws in place to protect religious freedom — we don’t need to put those in this Bill and I won’t be voting for any amendments.”

The Bill is expected to pass the Lower House by the end of this week, paving the way for same-sex couples to marry in Australia from January.

Prime Minister Malcolm Turnbull has backed changes that would guarantee charities are not affected and allow civil celebrants to refuse to solemnise weddings.

But with 75 votes required to defeat conservatives’ amendments, Labor is expected to join forces with Green Adam Bandt, crossbenchers Rebekha Sharkie and Andrew Wilkie and Liberal MPs Warren Entsch, Mr Pyne and Mr Zimmerman to kill them off.

Mr Falinski told the Lower House he believed religious freedoms should not be dealt with in the same-sex marriage Bill, but rather through the inquiry to be led by former attorney-general Philip Ruddock that will report back by March.

“My distinct preference is for this discussion to be dealt with holistically, rather than piecemeal in a bill designed to give expression to people’s voice by expanding definition of marriage in law,” he said.