State leaders met in Canberra on Friday to consider the funding arrangement announced on Sunday, as well as disability care, Australia in the Asian century, the early childhood education national partnership, gang laws and the Royal succession.
But the schools funding deal was not signed, leaving Ms Gillard to try and get agreement by her longer range deadline of June 30.
"No jurisdiction was in a position to sign on Friday," she told reporters.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"We will continue discussions."
Under its new model, Labor is offering the states $14.5 billion in schools funding from next year, with the federal government to pay 75 per cent of the total and the rest coming from state coffers.
It also wants state education budgets to increase by three per cent a year, in return for a greater 4.7 per cent lift in federal money.
Ms Gillard said the leaders did agree that Australia needed a high quality education system.
The COAG did make some progress on disability, with the ACT and South Australia signing up for the longer term implementation of the national disability insurance scheme from 2018.
As well, the Northern Territory has agreed to host a launch site covering Tennant Creek.
Leaders also discussed the principles that will guide the way the disability care system will work.
"So some principles were agreed," Ms Gillard said.
COAG chair Victorian Premier Denis Napthine said there had been "considerable discussion" about the schools funding proposal, and the importance of getting the reform right.
"Ultimately there is more work to be done, with jurisdictions to examine the financial implications for each of their jurisdictions, and there will be ongoing bilateral discussions between jurisdictions and the commonwealth on those matters," he said.
One of the main opponents of Labor's schools funding split, Western Australian Premier Colin Barnett, said he would be part of further talks with Ms Gillard on the issue.
"We will stay in the discussions," he said. "But at the moment there is little to attract us."
Ms Gillard said she wanted to see WA schools benefitting from the extra resources and money being offered. Under the plan, WA would receive about $300 million over six years.
The leaders also discussed ways to tackle gang violence, organised crimes and illegal firearms and increase cooperation through proposed national gang laws.
"As organised crime and gangs become more and more sophisticated, it's necessary to make sure that across the country there is no place to hide and no loopholes," Ms Gillard said.
Dr Napthine said leaders had expressed a "very strong commitment" to fighting gang organised crime.
"COAG committed to further work by police ministers and attorneys-general to further develop agreed cooperative approaches to deal with criminal organisations and unexplained wealth," he said.
"There was also agreement with respect to examining issues associated with illegal firearms, and to strengthen existing firearms laws in regard to tracking of firearms and ballistics identification."
The COAG meeting also addressed the issue of the royal succession, ahead of the impending birth of a child to Prince William and the Duchess of Cambridge.
"This is Australia's part in ensuring in the future girls could become the monarch in the same way that boys can so there's no discrimination, and no discrimination against the monarch marrying a Catholic," Ms Gillard said.
All states and territories endorsed the commonwealth enacting legislation on the matter.
"Individual states can elect if they so choose to also enact their own legislation," Ms Gillard said.
This gives leeway to Queensland, which had initially objected to the commonwealth taking the lead on the issue.
"I think this provides a sensible way forward for all jurisdictions to operate under the commonwealth constitutional changes," Dr Napthine said.
Meanwhile, ACT chief Labor minister Katy Gallagher is confident her government can reach agreement with the federal government on schools funding by June 30.
South Australian Labor Premier Jay Weatherill was also hopeful a deal can be struck.
Tasmania Labor Premier Lara Giddings said her state hasn't signed up because there were final details to be worked out, although she supported the reform.
Queensland Premier Campbell Newman said state schools were his government's constitutional responsibility, not the federal government's.
"We are concerned by a number of things that are centralist in approach," he added.
Mr Barnett said he was worried about WA state schools having to report to Canberra.
Mr Newman said Queensland had put up $835 million over five years but the commonwealth was asking for the state, which has fiscal constraints, to raise $1.3 billion over six years.
"You can see there's a gap and I've got to go and work on it," he added.
NT chief minister Adam Giles said his door remained open but the current offer was not acceptable and the commitments required from the territory were "unsustainable."
"It's almost the case of death or Siberia," he said.
Dr Napthine and NSW Premier Barry O'Farrell are both keen to continue bilateral negotiations on schools.
National schools reform:
*negotiations on commonwealth's proposed reforms, including funding, will be ongoing
*states need to sign bilateral agreements by June 30 so schools get extra funding in 2014
National disability insurance scheme:
*agreement to implement full scheme in ACT, South Australia from 2018/19
*in-principle agreement for Northern Territory launch site in Barkly region from July 2014
*commonwealth to work bilaterally with other states to implement NDIS
*agreement on principles to guide the NDIS system interface*commonwealth to work with states on related injury scheme to support people suffering disability after accidents
Australia in the Asian century:
*COAG standing councils to report back October 2013 on engagement with Asia and strategies
*standing councils to also consider how to get started on other 29 white paper policy suggestions
Early childhood education:
*agreement on new national partnership agreement
*agreement offers $655.6 million in commonwealth funding over next 18 months
National response to gang violence, crime:
*agreement to ensure law enforcement agencies have the powers they need to act
*COAG justice standing council to examine options to fight nationally gang violence and organised crime
*improvements to improving intelligence, data and information sharing between jurisdictions
Public safety mobile broadband:
*more work needed to set up public safety mobile broadband capability for when disasters occur
Royal succession:
*hybrid model to implement previously agreed changes to the rules of succession
*states can now enact own legislation if they choose
*states agree to ask commonwealth to enact required legislation under constitution
