The travel advisory is "a result of the failure of Australian authorities to stand up against persistent demonisation, harassment and violence against Jews and Jewish institutions in Australia".
The centre sent at letter to Australia's US ambassador Kevin Rudd to tell him of its decision.
The centre's Rabbi Abraham Cooper said Jews, especially since the October 7, 2023, attack by Hamas on Israel, have been targeted around the world and and Australia was no exception.
"This latest attack comes within days of Australia voting for a UN resolution demanding Israel revert back to its indefensible pre-1967 War borders," Rabbi Cooper said.
"Such a resolution, far from strengthening hopes for peace only emboldens those who seek Israel's demise, who demean Jewish history, and who hate Judaism, Zionism, and Zionists."
Israel itself has a level two threat on Australia advising travellers to increased precautionary measures since the fire at the Adass Israel Synagogue at Ripponlea in Melbourne's southeast on Friday.
Australia, meanwhile, has told its citizens to reconsider their need to travel to Israel and the Occupied Palestinian Territories due to the ongoing war in Gaza.
Police have been criticised for being too slow to act against anti-Semitism as officers hunt the people who firebombed the synagogue on Friday.
The arson attack was the final straw in a terrible year for the Jewish community Australia's special envoy to combat anti-Semitism Jillian Segal said.
Jillian Segal says multiple factors have contributed to the rise in anti-Semitism. (Thomas Parrish/AAP PHOTOS)
The firebombing is being investigated as a likely terror attack with the Joint Counter Terror Team (JCTT) taking the lead as authorities hunt three suspects.
"The rise in anti-Semitism is just completely unacceptable but what we need now is a co-ordinated response," Ms Segal said on Tuesday as she called for strong action.
"We need to see policing where people are brought to justice and linked through to actual prosecutions and penalties."
The special envoy didn't pin the blame on the federal government following criticism the prime minister has been too slow to act, saying there were multiple factors that contributed to the rise in anti-Semitism.
"So far, we've not seen very serious penalties apply to anyone who has been arrested, whether it's been for flying a prohibited flag or anything like that," she said.
"That has set the tone of permissiveness in our community and that's been a combination of government, policing, enforcement, the court system and the community more generally."
The destruction from the arson attack was laid bare in photos from inside the charred building. (Yumi Rosenbaum/AAP PHOTOS)
Ms Segal welcomed strong condemnation from the federal government and the establishment of a dedicated anti-Semitism taskforce before meeting Prime Minister Anthony Albanese at Parliament House on Tuesday.
Testing laws to ensure perpetrators were held to account and education were key issues that would be raised in the meeting, she said.
It was an issue that needed to transcend politics, she added, as the coalition launched attacks against the prime minister for his response.
The terror declaration of the fire opens up a raft of extra powers for investigators including the ability to stop, search and seize people without a warrant as well as detain and question those they believe have knowledge of, or links to, the attack.
The JCTT is made up of state and federal police and ASIO officers.
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