Dozens of Palestinians fled their homes here Sunday in anticipation of another wave of demolitions that Israeli military officials warned will be carried out soon. Secretary of State Colin L. Powell said the United States opposes the demolitions and appealed to Israel to halt the destruction in the aftermath of a week of violence.

Israel's Supreme Court on Sunday rejected a petition from a Palestinian rights group seeking to stop the razing of homes in Rafah, which is located on the border between the Gaza Strip and Egypt. The three judges said the army had a "real, imminent need" that justified the demolitions.

A senior Israeli security official said the army was awaiting legal approval from the state attorney general's office before launching a new operation. "If we get a green light, we will move in," said the official, who could not be identified under the ground rules of the government briefing.

The official said the army had asked for permission to widen its security corridor from 100 yards to between 200 and 300 yards in a swath of territory where it says buildings are used by Palestinian gunmen and by smugglers ferrying arms and ammunition from Egypt to Rafah in deep tunnels. He would not estimate the number of buildings that could be destroyed, but Israel Radio reported that the army chief of staff, Lt. Gen. Moshe Yaalon, told the Israeli cabinet that hundreds more Palestinian houses could be demolished.

During three days last week, dozens of houses were destroyed in some of the most intense fighting between Israelis and Palestinians in the current conflict, which has continued for almost four years. Seven Israeli soldiers and 19 Palestinians were killed, according to the army, and U.N. relief officials who oversee this refugee camp said more than 1,000 people were made homeless.

Before leaving an economic conference in Jordan for Washington, Powell told reporters, "We oppose the destruction of homes, we don't think that is productive." He added, "We know that Israel has a right for self-defense, but the kind of actions that they are taking in Rafah, the destruction of Palestinian homes, we oppose."

"The United States is anxious to do everything that it can to stop this cycle of strike and counterstrike that has resulted in the loss of so many lives within the last week," he said.

Early Monday, Palestinian witnesses said Israeli helicopter gunships fired rockets at two sites in Gaza City, hitting an office belonging to Palestinian leader Yasser Arafat's Fatah movement and another belonging to the Democratic Front for the Liberation of Palestine, a small militant faction. There were no immediate reports of casualties. On Sunday evening, Israeli troops killed three Palestinians trying to plant a bomb along a border fence between Israel and Gaza, Israel Radio reported, according to news services. The military said soldiers fired at suspicious Palestinians, and explosives they were carrying detonated, killing them.

Earlier Sunday, in the refugee camp here, Palestinian women grabbed undershirts and towels and stuffed them into plastic bags. Men pried off sinks, faucets, door frames and other valuable fixtures from their homes. Outside, trucks loaded with furniture jammed the streets.

Israeli troops had pulled back on Saturday, leaving a concrete moonscape pockmarked with piles of rubble. "That's my friend's house over there," said 12-year-old Ahmed Abu Tiyyur, pointing to a pile of concrete, shattered metal and broken glass. Then he pointed to a higher, nearer pile. "That house was demolished yesterday," he said.

Residents of Block O, one of the most ravaged neighborhoods in the camp, said Israeli soldiers had announced over a loudspeaker in fuzzy, crackling Arabic Sunday afternoon that they had 24 hours to evacuate. They said the warning had come from an Israeli outpost atop a distant mound of dirt at the base of the 26-foot-high steel wall inside the border. An army spokesman, Capt. Jacob Dallal, said there were no soldiers in the area Sunday and denied that warnings had been broadcast.

Some residents of Block O slept elsewhere when the fighting began Wednesday and returned to find their homes demolished. "I don't know where my house is," said Salim Redwan, 67, holding a shower faucet that he said was all he could retrieve.

About 670 newly homeless people took refuge at the Al Khansa school. At night they slept on thin mattresses in classrooms cleared of desks, or on the sand in the courtyard. Local resources for caring for the refugees were overwhelmed, said Rafah's governor, Majid Agha.

"In recent days the intensity of demolitions has seen a dramatic increase in the numbers of lost buildings in Gaza," Peter Hansen, the U.N. Relief and Works Agency's commissioner general, said in a statement. "Now UNRWA has the job of dealing with the human tragedy behind each demolition, the distressed children in its schools, the homeless families in need of basics like blankets, food and water, and the communities shaken by the stress of ceaseless conflict."

But Israeli officials have said the United Nations is exaggerating the number of houses destroyed and families displaced, saying many had left the area months ago when the fighting first intensified.

Prime Minister Ariel Sharon has proposed unilaterally withdrawing Israeli forces and Jewish settlers from Gaza. But Sharon has insisted that even after a pullback, the army would maintain its grip on the border with Egypt to prevent arms smuggling.

Israeli security officials say they are most concerned about the possibility that militants could bring Katyusha rockets and other medium-range weapons into the strip.

Frankel reported from Jerusalem and Tel Aviv.

Palestinian children stand amid the rubble of buildings demolished by the Israeli army in the Rafah refugee camp in the Gaza Strip, on the border with Egypt. Palestinians stand next to one of dozens of buildings razed last week. Israel says the buildings have been used by gunmen and for weapons smuggling.