Palestinian officials said two boys - aged 10 and 11 - were killed when Israeli tanks opened fire on them in separate incidents in the West Bank town of Nablus.
The confrontations come a day after Israel's lifting of its 10-day siege of the Ramallah headquarters of Palestinian leader Yasser Arafat, after pressure from the United States.
The withdrawal has been seen within Israel as an embarrassment for the country's Prime Minister Ariel Sharon, who has come in for serious criticism.
'Erroneous assessments"
Although most soldiers have left Ramallah after withdrawing from Mr Arafat's headquarters, they have maintained a military presence in the city.
Palestinian sources said some troops had set up a look-out in a house opposite Mr Arafat's office.
Several of Mr Sharon's ministers have now acknowledged problems with the siege.
Tourism Minister Yitzhak Levy also said the decision to descend upon Mr Arafat's headquarters was based on "erroneous assessments", while Housing Minister Natan Sharansky said it had not been understood what the US reaction would be as it prepares for possible conflict with Iraq.
Former Prime Minister Binyamin Netanyahu said Mr Sharon should have been even harder on Mr Arafat, while dovish politicians said the government had blundered in without thinking of the outcome.
Mr Sharon's government has also come under threat from two politicians who intend to challenge Defence Minister Binyamin Ben-Eliezer for the leadership of the Labour Party, a member of the national unity coalition government.
Both Haim Ramon, a member of parliament, and Haifa Mayor Amram Mitzna have both demanded that the Labour Party pull out of the government.
Mr Mitzna said: "I'm no less a patriot than many right-wingers, and no less a nationalist.
"It is possible and right to fight terror but we have to get out of the government to save this country, to save the party."
Mr Ramon also declared it was time to go. "We don't have any influence in this government," he said.
New incursions
On the streets, Israeli tanks made several incursions into Gaza, backed by helicopter gunships, and one Palestinian man was shot and killed.
A woman was reported to be in a coma after shells struck her Gaza home in an earlier attack.
An Israeli soldier was also killed and another seriously injured when gunmen fired from a building in Nablus.
It was unclear if that was related to the shooting of the two boys.
Meanwhile in Washington, President George Bush Monday has resisted efforts by Congress to commit his administration to moving the US embassy in Israel to Jerusalem.
To do so would implicitly recognise the city as the country's capital, a move sure to enrage Arabs who want to make part of the city into the capital of a Palestinian state.
President Bush signed the bill, including the controversial clause, but said his administration's policy on Jerusalem had not changed and that congress could not dictate his foreign policy.
A government spokesman said that the future of Jerusalem, which has been partially occupied by Israel since 1967 and claimed by both Israel and the Palestinians - should be decided in negotiations.