RAFAH, Gaza Strip (Reuters) - Israeli gunfire killed a Palestinian girl at a U.N.-run school Monday, witnesses said, and militants shelled Jewish settlements in response, straining a de facto truce that has raised hopes for peace.

The incidents punctured the relative calm that has settled over the Gaza Strip over the past two weeks, following new Palestinian President Mahmoud Abbas´s efforts to coax gunmen into a cease-fire ahead of a planned Israeli pullout this summer.

Hamas launched mortar bombs and makeshift Qassam rockets at the Gush Katif settlement bloc after the girl´s shooting, causing no casualties, and a spokesman for the Islamic group said further violence would depend on Israeli military actions.

Earlier, witnesses in Rafah refugee camp in the southern Gaza Strip said 10-year-old Noran Deeb was killed by gunfire from an Israeli army post down the road while she and classmates were exercising in their schoolyard during morning assembly.

"Two girls fell to the ground, one was hit in the head and the other in the hand," teacher Mazen al-Ghandour told Reuters.

An Israeli military source said the army was not aware of its forces being involved in any shooting near the position on the border with Egypt, where soldiers and militants have often clashed during the 4- year-old Palestinian uprising.

"We are continuing to look into the report and the army plans to investigate in cooperation with the Palestinians," the source said.

A Reuters correspondent visiting the blood-stained schoolyard said it did not appear that Israeli soldiers some 600 meters (yards) away could have seen into the compound from their position behind high walls.

Witnessess said there were no confrontations between soldiers and gunmen at the time of the shooting.

"We heard Abu Mazen (Abbas) talking about redeployment. We heard talk about a cease-fire. But it seems there is nothing like that on the ground," the dead girl´s mother said.

"My daughter was lovely. Today she went to school earlier than usual. She said she wanted to play with her schoolmates before class."

WEST BANK PULLBACK TALKS

Abbas´s representative, Mohammed Dahlan, and Israeli Defense Minister Shaul Mofaz planned to meet later in the day to try to finalize an Israeli troop pullback from West Bank cities.

Palestinian security sources said the talks, following a meeting between the two men Saturday, would go ahead but Dahlan would voice his displeasure over the killing of the schoolgirl.

The sources said Ramallah, where the Palestinian Authority has its headquarters, was likely to be the first West Bank city to be handed over to Palestinian security forces. Mofaz said on Sunday pullbacks could begin within days.

The Israeli army has checkpoints around West Bank cities and has mounted frequent incursions in pursuit of wanted militants, operations the Palestinian sources said would end on condition Abbas kept the gunmen in check.

Last week, Palestinian security forces fanned out across the southern Gaza Strip, building on an earlier deployment in the northern part of the territory, following talks between Israeli and Palestinian officials.

But Rafah residents told Reuters the paramilitary police had not been stationed near the army post they said had fired at the school Monday. (Additional reporting by Nidal al-Mughrabi in Gaza and Mohammed Assadi in Ramallah) (© Reuters 2005. 01/31/05)