Friday's violence erupted following Muslim midday prayers.
One Palestinian was killed in Tulkarem and one in Hizme, both in the West Bank. Confrontations elsewhere in the West Bank and Gaza Strip left dozens injured, hospital doctors said.
``The cease-fire doesn't apply to us,'' said Ali, a 17-year-old rock thrower in Hebron, in the West Bank. Overall, the clashes weren't as intense as the past few days, but demonstrated that many young Palestinians were still prepared to take to the streets.
A Thursday car bomb that killed two Israelis in Jerusalem and firefights in Palestinian territories came only hours after a cease-fire was reached and threatened to destroy the agreement. During the past five weeks of fighting, such outbursts have often touched off retaliatory violence.
Yet Israeli Prime Minister Ehud Barak struck a conciliatory note Friday.
``We will persevere in our efforts for peace and we will devote all our strength to it,'' the prime minister said. ``We are strong enough to stand on both fronts: the battle for peace and the struggle against violence and terror.''
Over the past two days, both sides have taken steps to implement the truce - Israel has pulled back tanks from Palestinian cities, and Palestinian police have restrained rock-throwing youths.
``We're doing our best,'' Nabil Shaath, a senior Palestinian negotiator, told CNN. ``It's much calmer today (in the Gaza Strip) than any day before.''
Three Israeli soldiers were killed in fighting Wednesday in addition to the two Israeli civilians who died in Thursday's bombing - events that normally prompt a swift and powerful Israeli military response.
``It's true that the gunfire continues and it's true that there are still clashes,'' Danny Yatom, Barak's top adviser, said on Israel radio. ``At the same time, I believe, from what I know, that the Palestinians are trying to calm the situation.''
Both sides said events on Friday and Saturday would provide evidence on whether the cease-fire agreement was being implemented.
Barak and Palestinian leader Yasser Arafat were expected to make simultaneous announcements Thursday afternoon formally declaring the truce.
But the announcements were postponed, the car bomb exploded shortly afterward, and neither leader has publicly declared the cease-fire.
On Friday, Arafat told CNN that there never was a deal for the two leaders to make televised announcements, the network reported. He said the Palestinians met their commitments by issuing a statement Thursday that called for Palestinians to ``stick to peaceful means'' when demonstrating.
The Israelis clearly expected more. The government invited journalists to a news conference Thursday to hear Barak, then canceled the event when it became clear that Arafat was not prepared to make a statement at the same time.
The latest truce was worked out by former Israeli prime minister Shimon Peres and Arafat before dawn Thursday. In the afternoon, a stolen Mazda car loaded with explosives detonated on a narrow residential street, less than 200 yards from the crowded Mahane Yehuda market, scene of several previous bombings.
One of those killed was Ayelet Hashahar Levy, 28, daughter of a prominent politician, Yitzhak Levy, head of the hawkish National Religious Party. Earlier in the day, he had toured Jewish settlements in Gaza to show their support for settlers.
``She is not the first (victim). May she be the last,'' said Levy.
A group identifying itself as the military wing of the radical Islamic Jihad claimed responsibility for the bombing in a statement faxed to The Associated Press office in Damascus, Syria.
The statement said the attack came ``in reply to the enemy's crimes against our Palestinian people,'' and vowed more attacks.
Arafat, speaking in Gaza on Thursday night, condemned the car-bombing attack, saying: ``We are against it completely.''
More than 160 people have been killed in five weeks of Israeli-Palestinian fighting, the worst violence since the sides began peace negotiations in 1993. Most of those killed were Palestinians.