In a strongly worded letter to Prime Minister Scott Morrison, Victorian Premier Daniel Andrews described the Commonwealth’s school funding agreement as “fundamentally flawed”.

The letter, which was sent ahead of this week’s Council of Australian Governments and Education Council meetings, urges the federal government to increase funding for public schools.

“If the Commonwealth is serious about improving student learning outcomes then it needs to do its share to adequately resource all Victorian schools,’ Mr Andrews wrote.

Independent Schools Victoria chief executive Michelle Green accused the state government of playing “fast and loose with parents”.

“We have been urging the Victorian state government to sign because our members are dependent on this agreement,” she said.

The federal government has previously threatened to withhold billions of dollars of funding earmarked for Australian public and private schools next year if states refuse to sign up to its new education funding deal.

But the Victorian government says it has received advice that says the federal government can continue to fund Victorian schools, regardless of whether an agreement is in place.

“I call on your government to start processing school funding payments for Victoria in 2019 now, rather than threatening to cease funding Victorian schools,” Mr Andrews said.

Ms Green is concerned the Victorian government’s advice could be tested and found to be wrong. She said this could lead to schools missing out on vital funds when an interim funding agreement expires on December 31.

“Schools rely on government funding; some would not have enough to continue,” she said.

“They are hiring staff, making plans for next year. This sort of uncertainty does not help. Never to my knowledge have we got to this stage without having a signed agreement between state and Commonwealth."

Federal Education Minister Dan Tehan said the federal government had been negotiating in good faith with every state and territory to finalise school funding agreements and provide certainty to schools and parents.

"Leaking letters to the media is not acting in good faith," he said.

“The Victorian government shouldn’t be risking the education of more than 950,000 Victorian school students by playing political games.”

Victoria and Queensland are the only states that have not yet signed up to the Gonski 2.0 agreement. The federal government had set a December 7 deadline.

Victoria has promised to significantly boost Victoria’s contribution towards the Schooling Resource Standard – the bedrock of the Gonski review into school funding which measures how much funding every school needs to supports students.

Victorian Education Minister James Merlino has committed to lifting Victoria’s contribution from 66 per cent, the lowest share in Australia, to 75 per cent.

But in order for a deal to be struck, he says the Commonwealth must boost its share from 20 to 25 per cent.

“There is something fundamentally unfair in a proposal from the Commonwealth where government schools get to 95 per cent of the Schooling Resource Standard and non-government schools get to 100 per cent and beyond,” Mr Merlino said.

“There is no reason, no fairness, it is completely illogical.”

Federal Education Department modelling has found that lifting the Commonwealth's share to 25 per cent would cost an additional $25 billion by 2023.

A spokesman for Catholic Education Melbourne said the Andrews government should negotiate with the Commonwealth in a constructive and positive way.

"It is not reasonable to leave such uncertainty about when funding will flow for Catholic schools for 2019."

The National Catholic Education Commission warned that Victoria's pursuit of a more favourable funding deal risked unravelling agreements that had already been signed by other states.

A spokesman for the commission said these states would push to re-negotiate their agreements if Victoria got a better deal.

Australian Education Union Victorian branch president Meredith Peace said she supported the Andrews government’s decision to push for additional funding for public schools.

“We have long argued that the Morrison government’s funding model is unfair, not needs-based and directs most of the federal money to those schools who least need it,” she said.

She said it would be "surprising and unprecedented" if money stopped flowing to Victorian schools.