At least three Israelis have been killed and many injured in shooting and stabbing attacks in Jerusalem and central Israel, Israeli police say.

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 fortnight.

Several attackers and at least 17 other Palestinians have been killed in the upsurge of violence.

Police said officers arrived at the scene of Tuesday's bus attack and shot the attackers, killing at least one.

Elsewhere in the city, a man ran over three people at a bus station and then stabbed them with a knife, police said. One of the victims later died in hospital.

The attacker was shot by police. His condition is unclear.

Also on Tuesday, a Palestinian stabbed an Israeli man, moderately wounding him, at a bus stop in Raanana, north of Tel Aviv, police said. The attacker was captured and reportedly beaten by passers-by.

Later, an Israeli woman was stabbed and wounded in a second attack in Raanana, police said. The assailant fled, but was then arrested by police.

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.