ERUSALEM, Oct. 13 — In a message to Prime Minister Ariel Sharon before his planned visit to Washington this week, the Bush administration has criticized Israel for killing Palestinian civilians during its military operations and for maintaining crippling restrictions on movement in the West Bank and the Gaza Strip.

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The letter, delivered on Friday by the American ambassador to Israel, Daniel C. Kurtzer, was reported today in the local press and confirmed by senior Israeli officials; it followed similar expressions made publicly by Washington last week.

More Palestinian civilian deaths were reported today. A 3-year-old boy was killed during an Israeli Army raid in Rafah in the southern Gaza Strip in which a militant was also killed, and a woman was fatally shot near Jenin in the West Bank when soldiers opened fire on a taxi, Palestinians said.

The army said it was investigating the fatal shooting of a 60-year-old woman on Friday as she sat on the veranda of her house in the West Bank city of Nablus. Her son, who witnessed the shooting, said a soldier in a jeep had fired at the house without provocation.

In other violence today, two Palestinian gunmen who infiltrated Israel from Egypt were shot and killed by Israeli soldiers. In Bethlehem, an explosion near a public phone killed a local militant, and Palestinians said Israel was responsible.

The American message to Mr. Sharon expressed deep concern over what it described as a significant increase in Palestinian civilian deaths during recent Israeli Army operations. It asserted that Israel had failed to keep promises to ease restrictions on the movements of ordinary Palestinians hemmed in by checkpoints and blockades of cities and villages.

At the weekly meeting of his cabinet today, Mr. Sharon said that "Israel has great interest in easing conditions for Palestinians who are not involved in terrorism," but that by failing to crack down on militants "the Palestinian Authority does not enable Israel to move ahead with this policy as it wishes," a cabinet statement said.

A senior Israeli official said the American message repeated public expressions of American concern after an Israeli raid on the Gaza Strip town of Khan Yunis last week in which 17 Palestinians were killed and scores wounded.

In an early morning operation in Rafah today, Israeli forces blew up two houses while destroying a network of tunnels used to smuggle weapons from Egypt, the army said. The blasts damaged adjacent houses, and a 3-year-old boy, Tawfik Baraka, was killed by falling debris, Palestinians said. Eighteen people were reportedly injured. Ibrahim al-Ghuti, 26, who the army said was an armed militant, was killed by gunfire from Israeli tanks.

Near the Israeli border with Egypt south of Rafah, soldiers shot and killed two Palestinian infiltrators discovered near the farming community of Yevul, the army said. Palestinians said the gunmen were originally from Rafah.

In the West Bank, an Israeli tank fired on a taxi van traveling on a dirt road circumventing Israeli roadblocks southwest of Jenin, killing Yusra Sawalha, 40, and wounding two girls, Palestinians said. The army said it had no information on the incident.

In Bethlehem, an explosion at a public phone booth killed Muhammad Abayat, 27, a member of the militant Aksa Martyrs Brigades, an offshoot of the mainstream Fatah faction. The group accused Israel of responsibility and vowed to respond, saying it was no longer bound by a cease-fire in the area agreed as part of an Israeli troop withdrawal from Bethlehem in August.

In Nablus, hundreds of mourners joined the funeral of Shaden Abu Hijleh, 60, who was killed by Israeli gunfire as she sat on her veranda on Friday evening during a curfew.

Her son, Saed Abu Hijleh, 36, who was slightly wounded, said in a telephone interview that a soldier fired the fatal shots from the back of a jeep on the street near the house from about 30 yards away. Soldiers in passing jeeps usually enforced the curfew with concussion grenades or shots in the air, but the street was quiet on Friday, Mr. Abu Hijleh said.

"The back door of one of the jeeps opened, and without warning, without any provocation, without any threat to them — they could see us eye to eye — they opened automatic fire on us," he recalled. "Nine bullets penetrated the glass door where I was standing. They barely missed me."

Mr. Abu Hijleh was wounded by glass fragments, his father was slightly hurt by a ricocheting bullet, and his mother was mortally wounded in the chest, he said. "My mom was lying on the steps," he recalled. "I went over to her and said, `Mom are you O.K.?,' and she just looked at me with her eyes. I told her to say a prayer, and she died in my hands."