More than half of Australians think there should be more restrictions on the rights and freedoms of some people for the sake of national security.
The latest Essential poll, published on Wednesday, found only one in five believes existing laws strike the right balance in the fight against terrorism.
Older Australians, coalition supporters and independent voters are the biggest backers of tighter restrictions, as are nearly half of those who vote for Labor.
The survey was conducted during the same week the Turnbull government-brokered a deal with the states and territories to toughen parole and bail laws.
The leaders agreed to help keep people who have demonstrated support for or have links to terrorist activity behind bars, regardless of their offence.
It followed the deadly siege in the Melbourne suburb of Brighton, where one man was killed, a woman was taken hostage and three police officers were injured before the gunman was shot dead.
NSW, Victoria and South Australia have already put forward new anti-terrorism measures before a special COAG meeting on national security.
Victorian Premier Daniel Andrews said last week the country had reached a point where it needed to consider giving law enforcement more powers.
"It may mean taking the rights and freedoms of a small number of people (but) that is what will be needed in order to preserve and protect a great many more," he said.
A majority (74 per cent) of surveyed Australians agree the threat of terrorism on home soil has increased during the past few years.
Just less than half (46 per cent) believe the federal government should spend more on anti-terrorism measures.
A similar number approve of the way Malcolm Turnbull is handling the threat of terrorism in Australia - down nine per cent from October 2015, a few weeks after he replaced Tony Abbott as prime minister.
