The gunman was killed soon after carrying out the attack near police headquarters, close to the line dividing mainly Palestinian east Jerusalem from the mostly Jewish western sector of the city.
The shooting rampage comes at a time of increased Jewish visitors to the flashpoint Al-Aqsa mosque compound in Jerusalem for the holidays of Rosh Hashanah, which was last week, and Yom Kippur, which begins Tuesday evening.
Police said the 39-year-old assailant fired in the direction of a tram station in the area, seriously wounding a woman.
One of the women, a 60-year-old, was reported by medics to be in critical condition after being shot in her upper body.
Also Read
The attacker then headed toward the nearby neighbourhood of Sheikh Jarrah in Israeli-annexed east Jerusalem, where a number of upscale hotels are located, and got out of his car, police said.
As officers approached him by motorcycle, he opened fire on them.
Police returned fire and killed him, but two officers were wounded, including one seriously, they said.
Hadassah hospital later reported that two of the victims had died, without providing further details.
Israeli Prime Minister Benjamin Netanyahu, speaking at the start of a cabinet meeting on Sunday, saluted the police, saying they had "acted rapidly and very firmly against the terrorist, who was eliminated".
A spokesman for Palestinian Islamist movement Hamas, which runs the Gaza Strip, welcomed the attack.
Fawzi Barhoum called it "a natural reaction to the crimes and violations of the occupation against our people".
The Palestinian Islamic Jihad movement also praised that attack, calling it "heroic".
The Al-Aqsa mosque compound is holy to both Muslims and Jews, who refer to it as the Temple Mount.
Last year's Jewish high holidays led to clashes and marked the start of an upsurge in Palestinian gun, knife and car-ramming attacks.
Violence since October 2015 has killed at least 232 Palestinians, 34 Israelis, two Americans, one Jordanian, an Eritrean and a Sudanese national, according to an AFP count.
Disclaimer: No Business Standard Journalist was involved in creation of this content