Israeli Prime Minister Benjamin Netanyahu announced a "strong" and "firm" response to "terrorism" after the two Palestinian attacks in East Jerusalem, one of which killed seven people near a synagogue.

"Our response will be strong, swift and precise," Netanyahu told an emergency security cabinet meeting. "We don't want escalation, but we are ready for any scenario."

On Friday, a 21-year-old Palestinian shot bystanders near a synagogue in the Neve Yatsov neighborhood, killing seven people, and then killed himself. On Saturday morning, a 13-year-old Palestinian shot and wounded two Israelis in Silwan, near the walls of the Old City.

The fresh violence in east Jerusalem, a part of the city occupied and annexed by Israel, comes at a time of sharp escalation after the deaths of nine Palestinians on Thursday in an Israeli army operation in Jenin, in the West Bank, a Palestinian territory occupied by Israel in 1967.

Israeli forces are on alert and the military said it was increasing the number of people in the West Bank amid calls for restraint from abroad.

US Secretary of State Anthony Blinken is scheduled to arrive in Jerusalem and Ramallah on Monday and Tuesday, where he will discuss de-escalation measures.

Netanyahu, a representative of the Israeli right, returned to power in late December with the support of far-right and Jewish ultra-Orthodox parties.