Australia will strengthen immigration laws and crack down on groups that incite hatred under a series of counter-terrorism measures which have come into force.

The measures are a bid to combat the threat from home-grown terrorists. Prime Minister Tony Abbott announced the nation's new anti-extremism strategy following the release of a government review into December's deadly siege at a cafe in Sydney's busy Martin Place plaza.

Man Monis, an Iranian-born, self-styled cleric with a long criminal history, took 18 people hostage inside the cafe.

He forced them to hold up a flag bearing the Islamic declaration of faith and demanded he be delivered a flag of the Islamic State (IS) group. Monis and two hostages were killed.

The government review found no major faults with multiple agencies that failed to detect Monis was a threat, despite the fact he was out on bail on sexual assault and accessory to murder charges.

But Mr Abbott acknowledged the system itself had failed, saying Monis should never have been allowed into Australia, should not have been out on bail and should not have been able to get a gun.

"It's clear that in too many instances, the threshold for action was set too high. And that the only beneficiary of that was the Martin Place murderer himself," Mr Abbott said.

"We cannot allow bad people to use our good nature against us."

The measures announced would revoke or suspend Australian citizenship for dual nationals who fight alongside terror groups overseas.

They would also axe welfare payments and consular services to those involved in terrorism and clamp down on "hate preachers," or groups that incite religious or racial hatred.

Australia's government raised the country's terror warning level in September in response to the domestic threat posed by supporters of IS.

In September, the group's spokesman Abu Mohammed al-Adnani issued a message urging attacks abroad, specifically mentioning Australia.

Mr Abbott warned the terrorism threat in Australia has escalated, noting that one-third of all terrorism-related arrests since 2001 have occurred in the last six months.

At least 110 Australians have gone to Iraq and Syria to fight alongside extremists, and the nation's security agency is juggling more than 400 high-priority counter-terrorism investigations - more than double the number a year ago, Mr Abbott said.