The government needs the support of the eight states and territories - all governed by the opposition Australian Labour Party - to enforce the new laws, which include jailing terror suspects without charge for up to two weeks and fitting them with electronic tracking devices.
Under the constitution, only state governments can allow suspects to be held longer than two days without charge.
State leaders in September gave unanimous support to a broad outline of the package but rejected an initial draft of the legislation and are currently considering a second draft.
Among their concerns are that judges would authorise detention orders, a move critics say oversteps the role of the judiciary.
Prime Minister John Howard told a meeting of lawmakers from his ruling centre-right coalition that he expects to show them the final draft of the legislation this week, once it was signed off by state leaders.
Queensland Premier Peter Beattie said on Tuesday state leaders are concerned that giving judges a role in authorising detentions could be unconstitutional.
Police can detain terror suspects
without charge for two weeks
"We certainly need more time; we won't be making the deadline today but we'll do this as quickly as we possibly can," Beattie told Australian Broadcasting Corporation radio.
"What we're trying to do is get sensible agreement that protects Australians from terror but also enables accountability and will not get knocked off in the High Court," he added.
Australian Capital Territory Chief Minister Jon Stanhope said state and territory leaders had raised several concerns about details of the legislation.
"To date, the prime minister has not responded to a single one that I'm aware of," Stanhope told ABC radio.
"I don't believe that the anti-terrorism bill in its current form should be supported by the Labor Party or any branch of the Labor Party as it stands. We're still negotiating it"
Australian Capital Territory Chief Minister
"I don't believe that the anti-terrorism bill in its current form should be supported by the Labour Party or any branch of the Labour Party as it stands. We're still negotiating it."
The proposed laws also came under fire from the government's human-rights watchdog, Human Rights and Equal Opportunity Commission President John von Doussa, who likened them to those in a police state.
Howard has said that he will not agree to any changes that water down the substance of the agreement reached in September.
The laws were drafted in response to the London bombings on 7 July that killed 52 people. Howard wants them passed before the southern city of Melbourne hosts the Commonwealth Games in March.
Australia will investigate claims of sexual abuse against Guantanamo Bay prisoner David Hicks after his father and a former detainee said he was taken from a US warship and abused in two 10-hour beatings before reaching Cuba.
"Our embassy in Washington will endeavour to follow up the credibility of these claims," Foreign Minister Alexander Downer said on Tuesday.
Hicks has been in Guantanamo
since his 2001 arrest
"We've had claims that he was tortured. We've had two American teams investigate those claims and they have come back with nil returns," said Downer, urging those making the allegations to provide evidence.
Downer said Australian consular officials had met Hicks several times and he had never raised the issue with them.
Hicks has spent three and half years in US military custody at Guantanamo Bay after being captured alongside Taliban forces in Afghanistan in late 2001.
Hick's father, Terry, told Australian Broadcasting Corp television that his son was blindfolded and beaten by Americans after being taken off a US warship in the Arabian Sea.
"He had two 10-hour beatings from the Americans," Hicks told the Four Corners current affairs programme on Monday night.
"I said to David: 'Sure they were Americans?' cause he said he had a bag over his head. He said, 'Oh look ... I know their accents, they were definitely American'," he said.
"[His attackers yelled] things like 'you Aussie kangaroo' and things like that, yeah, while they were beating and spitting on him and things like that, so he was called a traitor"
Ex-Guantanamo Bay detainee
A former Guantanamo Bay detainee, Briton Martin Mubanga, told the programme Hicks had told him he was helicoptered off the USS Peleliu aircraft carrier, blindfolded, beaten, spat upon, sexually abused and assaulted.
"[His attackers yelled] things like 'you Aussie kangaroo' and things like that, yeah, while they were beating and spitting on him and things like that, so he was called a traitor," he said.
Hicks' US military lawyer, Michael Mori, told ABC television he had witness accounts to back the latest claims.
Hicks, accused of fighting for the al-Qaida network, has pleaded not guilty to charges of aiding the enemy and conspiring to commit war crimes. His US military commission trial is set to start on 18 November.