The Greens are positioning themselves to reject the government’s Gonski 2.0 schools funding plans despite early signs they would wave it through because public schools’ funding would grow faster than that of private schools.

On Monday the Greens’ education spokeswoman, Sarah Hanson-Young, said the government plan was not backed up by enough funding and the party did not want to see any money cut from public schools.

The new formulation appears to provide support to Labor’s position that the policy cuts $22bn of funding relative to promised levels, although in absolute terms the policy increases funding by $2bn over four years or $18bn over 10.

Despite expressing scepticism of the government’s plan, the Greens have reserved their position until after a Senate inquiry that is taking submissions until 25 May and reporting back by 14 June.

When first announced, Greens leader Richard Di Natale said his party was “open to having a discussion with the government” on the policy if there was “significant investment” in public schools.

On Monday Hanson-Young told Sky News the Greens wanted “a fairer, more equitable model that looks after our public schools and the most needy schools”.

“But at first blush ... I don’t think the government’s model is backed up with enough funding,” she said.

“We don’t want to see any cuts to our education budget. We want to see our public schools looked after. We also want to see our neediest schools are getting the support first and foremost ...

“We don’t want to see any money cut from our public schools.”

Hanson-Young noted the Greens had many state members who had a responsibility to “find the best way forward in their state budgets to look after public school kids and kids most in need”.

“We know that we need more money on the table and a more equitable system.”

Compared with current levels the Gonski 2.0 policy delivers funding growth of 5.2% per student per year on average for government schools for the next four years; Catholic schools get 3.7% per student per year and independent schools get 4.4%.

But compared with funding trajectories in legislation and needs-based funding agreements with the states, the policy cuts $22bn over 10 years.

The Turnbull government’s policy is opposed by Labor, the Australian Education Union (AEU) and the New South Wales Coalition government, which has written to school principals warning them not to rely on federal figures for their future budgets.

Greens senator Lee Rhiannon has endorsed the AEU campaign in a series of retweets urging the Greens not to “slash the budgets of NSW public schools”.

Greens senator Lee Rhiannon’s retweets of Australian Education Union tweets campaigning against Gonski 2.0 schools funding changes.

The NSW Teachers Federation has released a hit-list based on state government data that shows NSW public schools are set for a $846m cut in 2018 and 2019.

Despite advocating for higher funding levels, Hanson-Young did provide support for the central premise of Gonski 2.0 to slow the growth of wealthier independent schools’ funding.

“The fact rich private schools [that are] well and truly above their resource standard at the moment can continue to get more public money, more money at the cost of taxpayers while our poorest schools just will never catch up – I don’t see how that’s equitable at all,” she said.