Three Palestinians, including two attackers, were also killed.
The attacks in Jerusalem, including a deadly shooting and knifing spree on a bus and a violent hacking attack caught on video, escalated the monthlong unrest and raised the pressure on Prime Minister Benjamin Netanyahu to take action.
The government has been unable to stop the violence, carried out mostly by young Palestinians unaffiliated with known militant groups and apparently acting on their own.
"We will use, and not hesitate to use, all means at our disposal to restore calm."
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Netanyahu left a meeting of top security officials to deliver the speech, and quickly returned. The deliberations continued into the evening.
Channel 2 TV said measures under consideration include a deployment of Israeli soldiers in the streets of Jerusalem to assist police, surrounding Palestinian neighborhoods in the eastern part of the city with troops, stepping up demolitions of attackers' homes, and stripping the families of attackers of their residence rights.
While Israel says the rumors are unfounded, clashes have quickly spread across Israel and into the West Bank and Gaza Strip.
Eight Israelis have died in a string of stabbings, shootings and the stoning of a car, while 29 Palestinians including 12 identified by Israel as attackers have been killed. In new bloodshed, a 27-year-old Palestinian man was shot dead in a protest in the West Bank town of Bethlehem.
The attacks have caused a sense of panic across Israel and raised fears that the region is on the cusp of a new round of heavy violence.