Two were killed and 16 others were wounded when two assailants opened fire and stabbed passengers on a bus in Jerusalem.
Another died in a vehicle and knife attack elsewhere in the city.
Near-daily stabbings by Palestinians have left dozens of Israelis dead and wounded over the past two weeks.
Several attackers and at least 17 other Palestinians have been killed in the upsurge of violence.
Israeli PM Benjamin Netanyahu will convene an emergency session of the security cabinet on October 13 to discuss the surge in violence.
The militant Palestinian Islamist movement Hamas, which dominates the Gaza Strip, praised the “heroic operations in Jerusalem and greets the heroes who carried them out”.
In the bus attack, the two assailants shot several passengers and stabbed others after boarding the vehicle in East Talpiot, a district in East Jerusalem also known as Armon HaNetziv, police said.
A security guard was able to overpower one of them and shoot him, Israeli media said. The second assailant then reportedly locked the bus doors in an attempt to stop police from boarding it and passengers from escaping, but police opened fire from outside and shot him.
Police said one of the attackers was killed and the other seriously wounded.
Minutes later, a man ran over three people with his car at a bus station in the Geula district of West Jerusalem. He then got out of the car stabbed them with a knife, police said. The attacker, identified as a resident of East Jerusalem, was shot by police. His condition is unclear.
Earlier in the morning, a Palestinian stabbed an Israeli man, moderately wounding him, at a bus stop in Raanana, a town north of Tel Aviv, police said. The attacker was captured and reportedly beaten and seriously injured by passers-by.
Not long afterwards, at least four other people were wounded in another knife attack in Raanana, police said. The assailant fled, but was then arrested by police.
Police identified both of the attackers in Raanana as residents of East Jerusalem.
Tensions between Israelis and Palestinians have escalated since last month, fuelled by clashes at a flashpoint holy site in Jerusalem, in the West Bank, and across the Gaza border, as well as the wave of stabbings.
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