The federal government and Labor want to protect lesbian, gay, bisexual and transgender students in religious schools but can't agree on how best to do so.
Faith-based schools could still have the right to discriminate against gay and transgender students into 2019 after the coalition and Labor failed to reach a deal on law changes.
But Labor Senator Kristina Keneally says her party is still open to negotiations with the government, as the final federal parliament sitting week for the year draws to a close.
"We have another day of parliament," Senator Keneally told ABC Radio on Wednesday evening.
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