GAZA CITY, Gaza Strip — Israeli warplanes and gunboats blasted more than two dozen Hamas targets Saturday, including weapons storage facilities, training centers and leaders' homes as Israel's offensive against Gaza's Islamic militant rulers entered a second week.

There were tentative signs that the current phase of fighting may be nearing an end. Most of the airstrikes targeted empty buildings and abandoned sites, suggesting Israel may be running out of targets.

Ground troops massed on the border, waiting for a signal to invade Gaza, but international cease-fire efforts were also gaining momentum.

French President Nicolas Sarkozy is visiting the region next week, and President George W. Bush and U.N. chief Ban Ki-moon both spoke in favor of an internationally monitored truce.

Israel launched the offensive on Dec. 27 in response to intensifying rocket fire by Hamas militants in Gaza. The operation has killed more than 430 Palestinians, including dozens of civilians, according to Palestinian and U.N. counts. Four Israelis have also been killed, and rocket attacks on southern Israel persist.

In the latest attacks, the Israeli army struck the homes of two Hamas operatives, saying the buildings were used to store weapons and plan attacks. Hamas outposts, training camps and rocket launching sites also were targeted, it said.

The army also struck the American International School, the most prestigious educational institution in Gaza. The school is not connected to the U.S. government, but it teaches an American curriculum in English.

The airstrike demolished the school's main building and killed a night watchman. Two other Palestinians were killed in a separate airstrike, while four others, including a midlevel militant commander, died of wounds sustained earlier, Gaza health officials said.

Early Saturday, it dropped leaflets in downtown Gaza City ordering people off the streets.

Palestinian militants fired six rockets into southern Israel, lightly wounding one person, police said. One rocket struck a house in the city of Ashkelon, police said.

The Israeli airstrikes have badly damaged Gaza's infrastructure, knocking out power and water in many areas and raising concerns of a looming humanitarian disaster.

Israel briefly opened its border Friday to allow nearly 300 Palestinians with foreign passports to flee the besieged area. The evacuees told of crippling shortages of water, electricity and medicine.

Maxwell Gaylard, U.N. humanitarian coordinator for the Palestinians Territories, said some 2,000 people have been wounded in the past week and a "significant number" of the dead were women and children. "There is a critical emergency right now in the Gaza Strip," he said.

Israel denies there is a humanitarian crisis in Gaza and has increased its shipments of goods into Gaza. It says it has confined its attacks to militants while trying to prevent civilian casualties.

While ground troops remained poised to enter Gaza, Israel also has left the door open to a diplomatic solution, saying it would accept a cease-fire if it is enforced by international monitors.