The Minister for the National Disability Scheme, Bill Shorten, has reached a deal with the states and territories to break a logjam over disability reform.

This paves the way for the government and opposition on Thursday to pass the legislation for tightening the NDIS, aimed at containing its costs and putting it on a sustainable long-term basis.

Shorten has had extensive negotiations to win Coalition support for the legislation.

In a statement on Wednesday, Shorten and the chair of the Council for the Australian Federation (CAF), South Australian Premier Peter Malinauskas, said the federal and state governments had agreed to a number of proposed amendments to the NDIS bill now before the Senate. These would strengthen how states and territories worked with the Commonwealth on NDIS reforms after the legislation was in place.

They included faster timeframes for approving NDIS rules, a new dispute resolution approach to escalate issues to first ministers, and a move from unanimous to majority first ministers’ support for any significant rules.

“These changes fully respond to the concerns originally raised by CAF on the legislation,” Shorten and Malinauskas said.

They said the changes would also protect the NDIS’s sustainability in the short to medium term and support the plan to reduce the cost growth to 8% by mid-2026.

“Critically, today’s agreement secures the support of states and territories for the government’s legislation and reform agenda and will help ensure the scheme is here for future generations of Australians.”

Malinauskas and Tasmanian Liberal Premier Jeremy Rockliff met Shorten in Moonee Ponds in his electorate earlier this month to discuss the states’ concerns.

Under the federal government’s NDIS reform plan, more responsibility for dealing with disability services will be put on to the states.

Shorten told a Wednesday news conference: “I just say to people with disability and participants, the message is that the states and the federal government are getting their act together and that people with disability and participants are not a political football”.

Asked about the amount of waste in the scheme, Shorten said this was hard to estimate.

“What I can estimate is that we can restrain the growth of the scheme to about 8%, and people will actually get better outcomes, better quality, better accountability.

"If I knew where all the waste was, we would stop it. But I’m confident that […] there’s $1-to-$2 billion at least, which we can shave off, which doesn’t affect people’s packages, which doesn’t affect quality, which doesn’t affect people’s access to the scheme.

"I know there’s overcharging going on. I know there are some providers who are putting in false invoices, and if we can clean up that, that will help contribute to it. ”

He said the fact the latest figure released last week showed expenses for the year to June 30 came in $600 million below what had been anticipated in the budget showed that already things were improving.