Debate on the package was expected to be held on Thursday after it passed the lower house in a marathon debate that finished just before 5am.

But a motion required to give approval for the bills to be debated so soon after they were introduced for consideration failed to go through the Senate on Thursday.

Government senators had indicated they would move to overturn the amendments in the upper house, due to it changing the nature of the original bill.

Moderate Liberal Andrew Bragg indicated he was prepared to cross the Senate floor in line with five of his lower house colleagues to uphold amendments protecting transgender children.

The government, therefore, was unlikely to have the numbers to pass the bill in the form it wanted despite last-minute talks with stakeholders to determine the future of the bill.

The bill is expected to be sent to another inquiry that will investigate the consequences of the amendments, which scrap protections for religious schools being able to discriminate against students on the basis of gender identity.

Senator Bragg told AAP he supports the idea of a religious discrimination bill and welcomed the inquiry.

“That is the policy of our government and that’s what I want to see,” he said.

“But I also want to see discrimination eliminated against students and teachers in schools.”

Conservative MPs expressed concerns about what the provision’s removal would mean for same-sex schools trying to accommodate transgender children.

Thursday was the last day the Senate will sit before the federal budget on March 29, which is expected to be the second-last upper house sitting day of this term.

Attorney-General Michaelia Cash refused to confirm whether the government will bring it back for debate before the election.

She told parliament the government was committed to protecting people of faith from discrimination.

Senator Cash also took aim at non-government amendments that passed the House of Representatives early Thursday morning after five Liberal MPs crossed the floor.

“Do you know what happens when you rush something and don’t consider the consequences? You can make mistakes,” she told the chamber.

“(The amendments) have the potential impact of increasing the grounds of discrimination against students.”

Australian Christian Lobby national director of politics Wendy Francis said the bill should be withdrawn due to the changed position.

She told AAP the lobby has been in touch with all government senators.

“The rights of religious schools in this country will be significantly diminished if this passes,” she said.

“Taking away protections for Christian schools is a price too high to pay for the passage of the religious discrimination bill.”

LGBTQ+ advocacy group Equality Australia called for the Senate to approve amendments preventing existing anti-discrimination laws being overridden.

Labor frontbencher Katy Gallagher said Thursday’s disarray showed the government failed to appropriately consult on the legislation despite Labor supporting the principle of religious protections.

“We said from the get-go we were keen on and supportive of a bill to ensure religious protection … but we also said it shouldn’t come at the price of someone else’s rights,” she told the ABC.

“(But) the bill was not genuinely about bringing people together in the end, this prime minister used that as a weapon to politically campaign and wedge (and) that’s really unfortunate.”