The New South Wales government has given a temporary reprieve to an estimated 20,000 vulnerable Australians who faced the loss of legal support due to federal funding cuts.

But the sector is warning the federal government’s looming cuts will still threaten access to justice for tens of thousands of people in other states, unless the decision is reversed in next month’s budget.

The community legal sector has long warned that cuts of 30% to federal funding would cripple already-stretched services.

The sector provides legal advice to 215,000 vulnerable clients across the country, including family violence victims, the homeless, those with a disability, non-English speakers, ageing Australians and low-income earners.

The cuts will come into effect in July, although the attorney general, George Brandis, maintains the government has made new investments in the sector, which far outweigh the forecast reductions.

On Wednesday, NSW became the latest state government to offer a rescue package to community legal centres.

The state’s new attorney general, Mark Speakman, announced a $6m boost in the next two years.

The package will maintain current funding levels in the first year, and a review will determine how the remaining money is distributed in the second year.

The funding will save lawyer positions and prevent the closure of already-stretched legal services, including in regional areas, where support services are not widely available.

But the package will not solve the funding crisis in the sector, according to Community Legal Centres NSW chair, Linda Tucker.

“Close to 20,000 extra people who would have been turned away each year will now have access to the legal assistance they need,” Tucker said.

“While this is a step in the right direction, given the scale of unmet need – tens of thousands of people turned away each year – it is imperative that today’s decision is built on by federal, state and territory governments across Australia. The funding crisis continues in this sector,” she said.

In 2014, the Productivity Commission found the sector was chronically underfunded, that federal investment had been “ad hoc”, and that there was a mismatch between areas of greater disadvantage and the placement of centres.

The commission found the lack of funding was creating gaps in the ability for Australians to access justice.

It recommended an injection of $200m from federal and state governments, and said every $1 spent on the sector saved the community $18.

The National Association of Community Legal Centres estimates that, even without the looming federal cuts, services are turning away 160,000 people each year due to a lack of resources.

Prior to Wednesday’s announcement by the NSW state government, the association estimated the federal cuts would cause another 64,000 people to be turned away nationally.

The association’s chief executive officer, Nassim Arrage, welcomed NSW’s decision, but said all levels of government need to “provide their fair share”.

“Funding for CLCs is the responsibility of both state/territory and federal governments,” he said.

“The recommendation of the Productivity Commission that involves maintaining current funding levels plus $200m for legal assistance nationally is a good starting point to determine what each contribution should be.”

A spokeswoman for Brandis did not say whether the cuts would be reversed.

But she said the government supports the “important work of the legal assistance sector” and was already providing substantial funding.

“Even in a resource-constrained environment, the Australian government is providing over $1.6bn for legal aid, community legal centres and Indigenous legal assistance between 2015 and 2020,” a spokeswoman said.

“On top of this, the Turnbull government has provided an extra $45m for frontline legal assistance services as part of its $200m investment to reduce violence against women and children.”

The spokeswoman said that $16.5m of that funding was going directly to community legal centres. She said the investment far outweighed the forecast reductions.

She said total commonwealth funding to NSW community legal centres had increased by 60% since 2010, from $6.8m in 2010-11 to $11.5m in 2016-17.