The United States is reported to have successfully pressed Israel to curb its strikes against Palestinian militants in an effort to encourage progress in peace negotiations.
The girl was reportedly shot from across the border
The move is designed to give Palestinian leaders time to broker a suspension of violence by radical militant groups, according to Israeli newspapers and the Reuters news agency.
But Israeli officials reportedly said they would only be given six weeks and the army would continue to attack militants described as "ticking bombs".
Palestinians have blamed Israel's aggressive policy against the militant group Hamas for an upsurge in violence that has claimed more than 50 lives since the unveiling of the international peace plan known as the roadmap two weeks ago.
On Tuesday night a seven-year-old Israeli girl died in a shooting attack near Israel's border with the West Bank.
ROADMAP MAIN POINTS
Phase 1 (to May 2003): End to Palestinian violence; Palestinian political reform; Israeli withdrawal and freeze on settlement expansion; Palestinian elections
Phase 2: (June-Dec 2003) Creation of an independent Palestinian state; international conference and international monitoring of compliance with roadmap
Phase 3 (2004-2005): Second international conference; permanent status agreement and end of conflict; agreement on final borders, Jerusalem, refugees and settlements; Arab states to agree to peace deals with Israel
The BBC Jerusalem correspondent says the immediate Israeli response was less harsh than might have been expected.
An adviser to Israeli Prime Minister Ariel Sharon said that alongside peace efforts "our own battle with the terrorists will have to continue".
But speaking about suspending strikes against militants - which Israel calls "targeted killings" - an unnamed Israeli official told Reuters that it would "hold fire as much as possible".
"This is to demonstrate to all sides that Israel is serious about giving the current round of talks the best chance of succeeding and forestall Palestinian charges of sabotage," the official is quoted as saying.
The deal was reportedly worked out by the Israeli prime minister's chief of staff, Dov Weisglass, during talks in Washington to resolve disputes over the so-called roadmap peace plan which is strongly endorsed by President George W Bush.
Tuesday's attack happened just inside Israel when automatic gunfire was sprayed at a junction near the West Bank town of Qalqilya.
The attacker reportedly used a pneumatic saw to hack through the grill of a drainage canal in the eight-metre high security wall that Israel has built around Qalqilya.
Seven-year-old Noam Leibowicz was shot dead and her three-year-old sister, brother and grandfather were also wounded in the ambush.
The Al-Aqsa Martyrs Brigades, an offshoot of Palestinian leader Yasser Arafat's Fatah faction, and the Popular Front for the Liberation of Palestine-General Command (PFLP-GC) claimed responsibility for the attack in a joint statement.
Overnight, Israeli forces blew up the home of a militant fugitive near the West Bank city of Nablus. They also destroyed four houses where 65 people lived in the Rafah refugee camp in Gaza on security grounds.
The incidents come amid a flurry of diplomatic activity ahead of the expected visit on Friday
by US Secretary of State Colin Powell.
Palestinian Prime Minister Mahmoud Abbas - known as Abu Mazen - was due to hold further talks with Palestinian militant groups, after earlier meetings failed to secure a ceasefire.
Militant spokesmen say Abu Mazen has proposed the creation of a Palestinian national leadership, made up of representatives of all Palestinian factions, which would be discussed in detail on Thursday in Gaza City.
Meanwhile, Israeli and Palestinian security officials have been discussing a possible army
withdrawal from Palestinian areas reoccupied since the beginning of the uprising in September 2000.
The withdrawal would begin in the northern Gaza Strip.