Two federal ministers sparked outrage from the states with their criticism of the rollout.
"Our biggest issue with the vaccines at the moment is to make sure that the states and territories roll out the supply of the vaccines that they have," Tourism Minister Dan Tehan said.
He wants states to use their "stockpiles", especially to cover vulnerable groups.
Ministerial colleague David Littleproud said he wants states, particularly his home state of Queensland, to "pull their finger out" as frontline workers wait for the jab.
According to federal figures, NSW had used only half of the 190,610 doses it had received, and Queensland was at 55 per cent.
But NSW Premier Gladys Berejiklian says the reports are "not true".
She warned the only way of meeting the federal target of vaccinating the Australian population by October is for federal and state governments to work cooperatively.
"Our government wants to speed things up," she said.
Labor leader Anthony Albanese said Scott Morrison promised four million people would be vaccinated by the end of March and was 3.4 million short.
"It would be good if the federal government took responsibility for something," Mr Albanese said.
Concerns are also growing about what will happen to community immunity if states don't have the second dose available.
"If the Commonwealth can tell us what their supply is, we are more than happy to roll out the rest of that as quickly as possible," Queensland Deputy Premier Steven Miles said.
NSW wants the federal government to apologise to all state and territory governments.
"I find this very offensive," NSW Health Minister Brad Hazzard said.
"We are at the frontline of a war, NSW and the other public health teams, and we have been doing a very good job with our public health officials working hard."
The Queensland premier remains concerned about supplies of vaccines and the nursing home rollout, both of which are in the hands of the Morrison government.
Premier Annastacia Pałaszczuk wants the federal government to publish daily figures on the number of vaccinations and the supply of vaccines to each state and territory.
Ms Berejiklian called for a national vaccination plan and has put the Byron, Ballina, Lismore and Tweed areas on "extra high alert" with new social restrictions until the end of Easter.
Prime Minister Scott Morrison said more than 650,000 people had been vaccinated nationwide and that would hit one million next week, as he hinges economic recovery plans on the rollout.
"We're on track for our first dose for everyone by October," he said.
"We're not relying like most countries in the world for vaccines to come from somewhere else."
The debate came as Queensland weighs up ending its lockdown on Thursday, as health officials make good progress on tracing cases linked to health workers.
Queensland reported two new local cases on Wednesday - one being a nurse from Brisbane's Princess Alexandra Hospital who had received her first vaccine dose, and the other is her housemate.
NSW also reported the case of a man in his 20s who last weekend attended the same Byron Bay venue as a hen's party which is linked to several COVID cases in Queensland.