Australian Federal Police taskforce Operation Avalite will be established to combat anti-Semitism following an arson attack on a synagogue in Melbourne that is now being investigated as a terror incident.

Prime Minister Anthony Albanese said the taskforce was being stood up in response to three recent anti-Semitic attacks: the attack on the Adass Israel synagogue in Ripponlea, an attack on Jewish Labor MP Josh Burns' electorate office, and an incident in Woollahra in Sydney where a car was torched and buildings vandalised with anti-Israel messages.

AFP Commissioner Reece Kershaw said the taskforce would give police expanded powers to investigate the incidents.

"Special Operation Avalite will be an agile and experienced squad of counterterrorism investigators who will focus on threats, violence, and hatred towards the Australian Jewish community and parliamentarians," Commissioner Kershaw said.

"Our world-class agencies will provide all the support necessary to find the perpetrators and ensure they face the full force of the law," Mr Albanese said.

Mr Albanese also committed to visiting the community where the synagogue was attacked.

The prime minister has faced immediate pressure to step up the government’s response from the opposition, who have accused the government of enabling anti-Semitism to go unchecked.

On Sunday, Mr Albanese committed federal funding to improving security measures at Jewish community sites.

Opposition Leader Peter Dutton vowed under a government he led he would fund the installation of armed guards at Jewish schools and synagogues, and tighten migration laws to explicitly stipulate that people who commit acts of anti-Semitism would have their visas cancelled.

The head of the Australian Security Intelligence Organisation (ASIO) however refuted suggestions the government could be blamed for recent attacks.

"I think that's a hard call to put something on government to stop people doing the wrong thing in our society," ASIO director-general Mike Burgess said.

He again urged commentators to be cautious in their language.

On Monday morning, Coalition MPs criticised the language of government ministers who had raised the issue of Islamophobia alongside anti-Semitism when discussing the arson attack.

Liberal senator and former ambassador to Israel Dave Sharma told Sky News "any time any senior minister mentioned anti-Semitism in the last 12 months they also mentioned a fictitious Islamophobia which was not going on".

"So they always had to create an equivalence every time they raise it," he said.

Shadow Home Affairs Minister James Paterson said the government should not be seeking to "balance communities' experience of racism against each other", because "both of those things are equally abhorrent but they are not equally prevalent".

The Islamophobia Register of Australia and the Executive Council of Australian Jewry track reported incidents of Islamophobia and anti-Semitism, respectively, using different methodologies.

Both groups reported a rise in discrimination against them in the immediate aftermath of the October 7 terror attack by Hamas.

Pressed on the issue on Monday afternoon, Mr Albanese cited the rise in anti-Semitism but declined to mention issues of Islamophobia.

"Anti-Semitism is a major threat. And anti-Semitism has been on the rise. We have seen incidents such as this that have been targeted specifically at the Jewish community," he said.