Coalition senator Sam McMahon will not withhold her vote in the chamber after her private bill was snubbed by the government.
The outgoing senator had said she reserved the right to withhold her vote if her bill on giving the Northern Territory the power to vote on euthanasia was not brought on for debate.
The government on Monday instead chose to allow debate on a One Nation bill seeking to outlaw vaccination mandates.
Senator McMahon told AAP it was still possible her bill would come up for debate next week or during parliament's February sitting and she would only withhold her vote in "extreme circumstances".
"I think it is fine to withhold your vote for issues you are very passionate about or that are important to the people you represent," she said.
"But a blanket withholding of your vote is very disruptive and a disservice to the Australian people.
"You would really have to think the government had done something horrendously wrong."
Liberal senators Alex Antic and Gerrard Rennick threatened to withhold their vote from the government over the issue of vaccine mandates.
The three senators, along with Liberal senator Concetta Fierravanti-Wells and Nationals senator Matt Canavan, were the only five to vote for the One Nation bill, which was defeated by 39 votes on Monday.
One Nation senators were not able to vote for the bill, appearing only via videolink.
Australian Associated Press