Peres and Arafat met earlier on Friday
The violence came as Israeli Foreign Minister Shimon Peres and Palestinian leader Yasser Arafat met for the first time in more than a month.
Israeli security sources say Palestinian gunmen opened fire near the Jewish settlement of Beit El, north of Ramallah, before escaping into Palestinian-controlled territory.
BBC Middle East correspondent Jeremy Cooke says the incident was reported at the end of a day which had been unusually quiet in the Palestinian territories.
But he adds that it is likely to provoke a military response from the Israelis, who will accuse Mr Arafat of failing to do enough to control the violence, and reignite the cycle of killings in the region.
Unofficial meeting
Mr Peres and Mr Arafat met on the sidelines of an economic conference on the Spanish island of Mallorca.
It was the first encounter between the two men since 26 September, when they issued a joint call for the ceasefire between Israel and the Palestinians to be observed.
Israeli Prime Minister Ariel Sharon has said he will not permit political negotiations with Mr Arafat until the current Palestinian violence ends.
An Egyptian delegate said the meeting was "serious and intense".
Mr Arafat told UK Prime Minister Tony Blair on Thursday that he would do everything in his power to maintain a ceasefire.
But our correspondent says that even if Mr Arafat is genuine about his desire to stop the fighting, it is clear that there are radical Palestinian groups determined to carry on the violent uprising against the Israeli occupation.
Israeli troops have maintained their presence in four Palestinian towns on the West Bank, which they entered after the assassination of Israeli Tourism Minister Rehavam Zeevi last month.
And Israeli tanks backed by bulldozers entered two separate parts of Palestinian-controlled territory in the Gaza Strip on Friday, according to Palestinian sources.
Witnesses said Israeli forces pushed 500 metres into Beit Lahiya village, destroying farmland near the Jewish settlement of Dugit.
Israeli tanks were also reported to have advanced 200 metres into Rafah in the southern Gaza Strip.
Possible role for Europe
Mr Peres and Mr Arafat shook hands before holding private talks in the company of Egyptian President Hosni Mubarak and Spanish Prime Minister Jose Maria Aznar.
The meeting could pave the way for a deeper involvement of the European Union in the Middle East peace process, with Spain due to take over the presidency of the EU in January, 2002.
Mr Peres and Mr Arafat held two hours of talks over lunch with the other leaders at the Formentor hotel, before emerging without comment.
Before leaving for Spain, Mr Peres said he would talk to Mr Arafat but played down the importance of the meeting.
"We were invited for an economic conference, and the purpose is not just to meet with Chairman Arafat. Mr Arafat will participate and I will participate," he said.
But Palestinian Cabinet minister Nabil Shaath said Mr Peres and Mr Arafat would discuss "ways to calm the situation and resume the negotiations."
The ongoing violence between Israel and the Palestinians will be discussed by Arab foreign ministers at a two-day meeting in Damascus this weekend.