A rearguard action by conservative Liberals to prevent the ACT and Northern Territory parliaments from considering assisted dying laws has failed in the Senate, with a Howard-era ban set to be overturned within days.

Liberals including South Australian Claire Chandler, Victorian Sarah Henderson and Tasmanian Jonathon Duniam opposed a private members’ bill during debate on Thursday, with the opposition putting forward last-minute amendments to thwart its passage.