The violence killed one Israeli and left several others injured this week.
Tzachi Hanegbi, chairman of Parliament's foreign affairs and defense committee which made the decision in a "special discussion" on Friday, said the additional forces "will help in returning order quickly" to Jerusalem.
There were minor protests on Friday in Jerusalem and in Hebron in the West Bank but on a much smaller scale than in recent days.
Most of the unrest was focused on Jerusalem's most sensitive holy site — a hilltop compound sacred to both Jews and Muslims. The compound is a frequent flashpoint and its fate is a core issue at the heart of the Israeli-Palestinian conflict.
It is known to Jews as the Temple Mount, site of the two biblical Jewish temples. Muslims revere it as the Noble Sanctuary, where they believe the Prophet Muhammad ascended to heaven.
Since Israel captured east Jerusalem from Jordan in 1967, Jews have been allowed to visit — but not pray — at the compound. Under an arrangement, Muslim authorities manage the site's religious and civilian affairs under Jordanian supervision, while Israeli police oversee security.
Unrest began Sunday on the eve of the Jewish new year holiday of Rosh Hashanah when Palestinians barricaded themselves inside the Al-Aqsa Mosque and threw rocks and firecrackers at officers. Police said pipe bombs were also found there.
Police entered the hilltop compound three days in a row to disperse Palestinians who had holed up inside the mosque with stockpiles of rocks and fireworks. The Israeli response sparked condemnations across the Arab world and concern that the tensions could spiral out of control.
Palestinian President Mahmoud Abbas condemned the clashes in particularly harsh language, claiming that none of Jerusalem's holy sites belonged to Israel.
Public security minister Gilad Erdan on Friday blamed Abbas for "incitement and lies" that led to violence. He said that by bringing explosive materials and rocks into the holy site, rioters had turned the "house of worship" into a "warehouse of terror."
On Friday, police put thousands of officers on patrol. It also banned Muslim men under the age of 40 from praying at the site in an attempt to curb violence as mostly younger Palestinians throw rocks at the site.