Clashes broke out Wednesday after Israeli soldiers raided a refugee camp near Ramallah in the West Bank and shot dead two Palestinians who tried to ram their cars into troops.
The Israeli military said three soldiers were wounded, including one seriously, but said it was investigating whether their injuries were due to stray fire from other troops.
Four Palestinians were wounded in addition to the two who were killed at the Qalandiya refugee camp in the occupied territory near a checkpoint at the entrance to Jerusalem, the Palestinian health ministry said.
"During an operation to make arrests of wanted Palestinians and to seize arms in Qalandiya refugee camp, two attempted car-ramming attacks were made against security forces in two different parts of the camp," the Israeli army said in a statement.
The Palestinian health ministry named the dead men as Ahmad Jahajha, 21, and Hekmat Hamdan, whose age was not disclosed.
Witnesses said clashes erupted during the raid and lasted for several hours.
Two cars were later seen with a large number of bullet holes in them in the camp.
Wednesday's raid came amid almost daily knife, gun and car-ramming attacks by Palestinians and clashes with Israeli soldiers since October 1.
The violence has killed 119 on the Palestinian side, 17 Israelis, an American and an Eritrean.
Many of the Palestinians killed have been attackers, while others have been shot dead by Israeli security forces during clashes.
Young Palestinians have grown frustrated with Israel's occupation and the complete lack of progress in peace efforts, in addition to their own fractured leadership.
In the Gaza Strip, Palestinian security and medical officials said that cross-border Israeli tank fire wounded three people, one seriously, after what the Israeli military said was an apparent roadside bomb attempt against an army border patrol.
- 'Hamas border post hit' -
The Palestinians did not identify their casualties.
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Eyewitnesses said the Israeli fire also hit a border observation post of the Islamist militant group Hamas, which controls Gaza.
An Israeli army statement said that no troops were wounded and shells were fired in response.
"I can confirm that artillery fire was used," a spokeswoman told AFP.
Earlier Wednesday, a Palestinian was wounded by Israeli gunfire at the border fence, Palestinian medical officials said.
On Tuesday, the United Nations voiced deep concern over an "unacceptable" wave of Palestinians attacking Israelis, but also criticised "excessive use of force" in response to the attacks.
"We continue to be gravely concerned at the unrelenting violence in the Occupied Palestinian Territory and in Israel," Cecile Pouilly, spokeswoman for the UN human rights office, told reporters.
"We call on both Israeli and Palestinian leaders to act decisively to de-escalate the situation."
Pouilly warned that although international attention appeared to be waning, "the level of killings, injuries and arrests has continued, with an average of one person dying every day".
On Wednesday afternoon, envoys of the international diplomatic quartet met senior Israeli officials in Jerusalem, the foreign ministry said in a statement.
"There was a long, serious and businesslike discussion on ways to bring the violence to a halt and bring back security," the Hebrew-language statement said.
"Both sides acknowledged that continuing the peace process is the real guarantee for achieving peace with security."
The quartet groups the United States, Russia, the United Nations and the European Union in an effort to broker an end to the Israeli-Palestinian conflict.
Israel announced last month that it was suspending until further notice diplomatic contacts with EU institutions over the bloc's decision to label goods imported from Jewish settlements.
But the European Union pledged to continue working for Middle East peace "in the quartet".