While Prime Minister Benjamin Netanyahu and president Mahmud Abbas have sought to avoid an escalation, frustrated Palestinian youths have defied efforts to restore calm and a wave of stabbings has spread fear in Israel.
A rocket fired by Gaza militants hit southern Israel today hours after clashes along the border saw Israeli forces kill seven Palestinians.
More clashes today killed another two Palestinians.
The rocket, for which there was no immediate claim of responsibility, caused no casualties. Israel regularly responds to rocket fire with air strikes, but had not done so by evening.
A 22-year-old Palestinian Israeli police said they shot yesterday after he opened fire at them in east Jerusalem's Shuafat refugee camp died today.
Clashes erupted after his funeral, and one Palestinian who tried to throw a firebomb at security forces was shot in the leg, police said.
The Gaza Strip had been mainly calm amid the week's unrest elsewhere, but clashes exacerbated fears that a wider Palestinian uprising, or intifada, could erupt.
After warning shots, troops fired "towards main instigators in order to prevent their advance and disperse the riot", a statement said.
Seven Palestinians were killed, including a 15-year-old, and 145 wounded, medics said.
Following today's funeral of one of those killed, hundreds of young Palestinians approached the border with Israel and began demonstrating.
At one point, unarmed Hamas security forces in civilian clothes dispersed demonstrators peacefully, witnesses said.