The federal government expects to know within days whether Victoria will sign up to Labor's schools funding plan.
Prime Minister Kevin Rudd and Education Minister Bill Shorten on Tuesday met with Victorian Premier Denis Napthine in a bid to convince him to get on board the Better Schools Plan.
Mr Shorten said the talks were "constructive" and "positive" but there were more intensive discussions to come in following days.
He was focused on achieving a "mutual win-win" for children in Victoria's state schools, not on setting a deadline for Victoria.
"There's no doubt in my mind that we'll know in the next few days," he told reporters in Melbourne after the meeting.
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Victoria stands to gain $4 billion in additional funding for its school system under the arrangement.
Mr Napthine described the talks as "fruitful", but said keeping school administration in local hands was also an important priority for the state's future.
"We want assurances from the federal government with regard to the management of our schools," he said.
"It's absolutely vital for us that our schools are managed by local school councils, local school principals and local school committees, rather than faceless bureaucrats in Canberra."
Earlier, the Catholic schools sector announced it was backing the government's national plan for schools improvement.
They join the independent schools sector in supporting Labor's funding offer, along with the state governments of NSW, ACT, South Australia and Tasmania.
Catholic schools stand to gain about $1.6 billion of the $15-plus billion in extra funding pledged by the government for the national schools system over six years.
Victoria, Queensland and the Northern Territory remain unconvinced, and although negotiations continue it's highly unlikely Western Australia will reverse its staunch opposition.
Getting Victoria across the line would be a major coup for the Rudd government as it prepares for an election as soon as August 31.
The coalition has vowed to scrap the government's schools plan unless an "overwhelming majority" of states sign on, and with Victoria on side Labor could argue it has the numbers.
Mr Rudd said if NSW could see the benefits of signing on, he was sure Victoria could too.
"I'm not sure that any mum and dad, or person in charge of a local parent community in a school in the state system in Victoria, would want to say goodbye to that," he said.
