One police car was torched as protesters on Friday tried to surge past police into the Roman Catholic Church of the Annunciation to get at the three Israelis - a man and two women. Police later removed the three and took them away for questioning.
Thirteen people were injured in the brawl, most lightly, Army Radio said.
Israeli officials sought to quickly defuse anger and said security at churches and mosques would be stepped up. The incident was prompted by personal grievances the three Israelis had against the state, they said.
Nazareth, in Israel's north, is the largest Arab town in the Jewish state. The incident lasted for more than two hours.
"This was not a (terrorist) attack and there was no specific intention to harm the Church of the Annunciation. We need to calm the situation as quickly as possible," Internal Security Minister Gideon Ezra said on Israel Radio from Nazareth.
Arab community leaders will meet on Saturday before joining a planned protest march in the town's streets.
An official at the Israeli prime minister's office said interim leader Ehud Olmert had spoken to Ezra and the chief of police and had ordered police to act with the utmost restraint.
Protests broke out after the
attack on the church
The church is one of Christianity's most important sites in the Holy Land. It was undamaged, officials said.
Arabs make up about 20% of the Jewish state's population. Nazareth has a sizeable Christian community.
Israeli Foreign Minister Tzipi Livni spoke to her Vatican counterpart to explain the situation and to say it was under control, a ministry official said.
Batons and stun
Police dispatched anti-riot and anti-terrorist units to the church. Local television showed them using batons and stun grenades to keep protesters back.
Channel 2 television said the three Israelis entered the church with a child's pram and started throwing firecrackers.
They also had gas canisters in the pram, it said. Army Radio said they were dressed as pilgrims.
Television reports said the man, a Jew, was a Jerusalem resident known to police and security services as having a history of threatening to attack churches.
While police said all three intruders were Jews, Israeli television said one of the women was Christian. Officials said one of the women was the Jewish man's partner.
Israeli Arabs are descended from families who stayed while hundreds of thousands fled or were forced out during the 1948 war of the Jewish state's founding.
They complain of discrimination and say the government fails to give the same funding to their towns and schools as it does to the Jewish majority. Israeli officials deny the accusation.
The Church of the Annunciation is built above a sunken grotto where, according to Roman Catholic tradition, the angel Gabriel told the Virgin Mary that she was to bear Jesus.