Mahmoud Abbas blamed the latest tensions on a series of visits by Jewish worshippers to Jerusalem's most sensitive holy site.
The visits to the contested site have helped fan strife in a region already on edge following last summer's bloody war in the Gaza Strip and the earlier failure of US Secretary of State John Kerry's Mideast peace efforts.
The shooting happened a day after a Palestinian from the West Bank city of Nablus stabbed and killed a 20-year-old Israeli soldier at a crowded Tel Aviv train station and another Palestinian assailant stabbed three people at a bus stop next to a West Bank settlement, killing a 25-year-old Israeli woman and wounding two others.
Much of the recent unrest has stemmed from tensions surrounding the holy site in Jerusalem's Old City, known to Jews as the Temple Mount and Muslims as the Noble Sanctuary.
Palestinians in east Jerusalem have carried out violent protests, alleging that Jewish zealots are secretly trying to gain control of the site. The Palestinians claim east Jerusalem, captured by Israel in 1967, as their capital.
In an address to thousands of people at his West Bank headquarters, Abbas accused Israel of trying to divide the mosque compound, comparing it to the experience of a holy site in the West Bank that was split between Jewish and Muslim sides after an Israeli settler gunned down 29 Muslim worshippers there 20 years ago.