Speaking in Sydney after yet another graffiti attack targeting the city's Jewish community and a day after visiting the fire-bombed Adass Israel Synagogue in Melbourne, Mr Albanese insisted Australia had been enriched by multiculturalism.
"That disgraceful act of burning of a synagogue sent shivers down the spine of all Australians," he told reporters at the Jewish Museum in Darlinghurst.
"We're a tolerant country, we're a country that is based upon respect for each other.
"The damage to the Torah that has been done is something that is just not what you would expect in a country like Australia."
The Adass Israel Synagogue at Ripponlea in Melbourne's southeast was set alight with people inside in a pre-dawn attack on Friday, destroying the building.
Security will be bolstered in Jewish neighbourhoods after graffiti including "Kill Israiel" (sic), was sprayed on buildings and footpaths in Woollahra, a Sydney suburb with a large Jewish community, in the early hours of Wednesday.
Mr Albanese on Wednesday defended taking four days to visit the Melbourne synagogue, saying he spoke with the Adass Israel president the same day and had been talking with the wider community and authorities the entire time.
Damage caused by the firebombing of the Adass Israel Synagogue. (Yumi Rosenbaum/AAP PHOTOS)
He said he was quick to declare it a terrorist event in his view.
"As prime minister, it's difficult to have personal views, you have to follow protocols," Mr Albanese said.
"But I made it clear, in my view, it was a terrorist event.
"I was very engaged with the Adass community."
There's a lot of anger in the Jewish community and the prime minister needs to act decisively, Executive Council of Australian Jewry co-chief executive Alex Ryvchin says.
"There's a sense we, as a society, and particularly the federal government, have allowed this to occur, that the government has presided over the most steep increase in anti-Semitism in Australian history," he told reporters.
A lot of difficult conversations were taking place in the community as people questioned their place in society following a spate of attacks, Mr Ryvchin said.
"They're questioning their future in Australia. They're feeling more safe abroad than they are in this country," he said.
Angry community members jeered the prime minister as he visited the synagogue on Tuesday, four days after the attack.
As he was leaving a woman called out: "Your words are cheap and late", and "You are late. You let this happen, buddy".
Another asked if he was "going to the Australian Open", referring to Mr Albanese playing tennis at the weekend.
Adass Israel members are using a nearby school's synagogue.
A full reconstruction of the destroyed synagogue could take years despite an outpouring of community donations and government funding.
The congregation of the Adass Israel Synagogue has vowed to rebuild after an arson attack. (Con Chronis/AAP PHOTOS)
Mr Albanese has committed to funding for the synagogue's rebuild and the restoration or replacement of scrolls damaged in the fire.
Victoria's government announced 15 community organisations would receive $950,000 in security funding.
Grants of up to $200,000 were available to Jewish community organisations to support the purchase, installation or improvement of security equipment at community facilities.
Three people are on the run following the arson after it was declared a likely terror attack on Monday, with investigators from Victoria Police, the Australian Federal Police and spy agency ASIO leading the probe.
Police are searching for two perpetrators, believed to be males aged between 15 and 20, who wore face coverings in the Sydney graffiti attack.
