A western Sydney man has been arrested over the synagogue blaze, which senior politicians described as an "attack on Australia".
The 34-year-old is accused of dousing the building's front door with flammable liquid and setting it alight, forcing 20 congregants to flee the East Melbourne synagogue on Friday night.
He was arrested in Melbourne's CBD on Saturday and charged with reckless conduct endangering life, criminal damage by fire and possession of a controlled weapon.
The man is due to appear in court on Sunday.
Detectives will investigate the accused man's intent and ideology to determine if the incident was an act of terrorism.
Police are also investigating another alleged act of anti-Semitism the same night, when protesters who had splintered from a larger demonstration allegedly smashed a window, flipped tables, threw chairs, and chanted "death to the IDF" outside Israeli restaurant Miznon.
Hours later, offenders spray-painted three cars and a wall outside a Greensborough business in Melbourne's northeast before setting fire to the vehicles, destroying one and damaging two.
The Israeli prime minister urged the federal government to "take all action" against those responsible.
None of the incidents have been declared terrorism-related but the force is increasing patrols around the synagogue and in the city's southeast.
Home Affairs Minister Tony Burke, former attorney-general Mark Dreyfus and Melbourne MP Sarah Witty met with the synagogue's Rabbi Dovid Gutnick, president Danny Segal and his wife on Sunday morning.
Mr Burke and Mr Dreyfus, who is Jewish, described the firebombing as an "attack on Australia" and the entire community.
"Let's make sure that this never happens again," Mr Dreyfus told reporters.
Mr Burke stopped short of declaring the alleged arson attack an act of terrorism, saying it would be up to Victoria Police to decide.
He refused to be drawn on Israel Prime Minister Benjamin Netanyahu's demand the Australian government "take all action to deal with the rioters to the fullest extent of the law"."
Mr Burke said he spoke with the Israeli Ambassador to Australia Amir Maimon on Saturday night as news filtered through of plans for him to fly from Sydney for the Sunday's meeting.
The ambassador took it as a signal of the government taking Friday's attacks very seriously, Mr Burke said.
Prime Minister Anthony Albanese condemned the synagogue arson as a "cowardly" act of violence and anti-Semitism and said the attacks on the restaurant and business were unacceptable.
The federal government has offered federal police and security and intelligence agency support to investigators.
"Those responsible for these shocking acts must face the full force of the law," he said.
The attacks come seven months after a blaze destroyed two buildings at the Adass Israel Synagogue in the city's south and forced worshippers inside to flee.
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