Australian police have charged a man in connection with an alleged arson attack on a Melbourne synagogue with worshippers in the building, the latest in a series of incidents targeting the nation's Jewish community.

Police in the southeastern Australian state of Victoria have arrested a suspect in connection with an arson attack on a synagogue in Melbourne on Friday night, during Shabbat prayers.

A man has been charged after a Melbourne synagogue was set alight with more than a dozen people inside, prompting a furious response from Israel's Prime Minister Benjamin Netanyahu. The 34-year-old man entered the grounds of the synagogue on Albert Street at 8pm on Friday, police said.