Labor, the Greens and disability groups say a unanimous vote in support of a royal commission into the abuse of people with a disability is a good first step.
But Labor leader Bill Shorten says it can't be left as a "token vote" and the government needs to now set up the inquiry.
On Monday in the House of Representatives, Prime Minister Scott Morrison personally moved a motion - which passed the Senate last week despite the government's opposition - backing the royal commission.
However, he said he needed to seek further advice from the states and territories on the issue before taking it any further.
He said he took the issue of abuse and neglect of people with disability very seriously.
Attorney-General Christian Porter has indicated he believes the government may need Letters Patent - a special legal instrument - from the states in order to hold the royal commission.
Mr Shorten says a timeline is needed, as the idea had been on the books for too long already.
Greens senator Jordon Steele-John said he had asked Mr Morrison for a timeline and the prime minister had told him: "I've said what I said."
"Not a good start," Senator Steele-John said.
Australian Associated Press