Despite the tough public line, Israeli officials have privately said they would consider other options to get the soldier back. Israel has released prisoners before in lopsided exchanges for captured citizens or the dead bodies of soldiers killed in battle.

Egypt has been leading international mediation efforts to solve the crisis, including talking to Syria, whose president, Bashar Assad, is believed to hold influence over Hamas' Syria-based political head, Khaled Mashaal. Turkey, a key Muslim ally of Israel, also has sent an envoy to Syria.

"We are dealing with more than one Middle Eastern government to see if the release of our serviceman can be secured. The fundamental principle is that his release must be unconditional," said Mark Regev, spokesman for Israel's Foreign Ministry.

Abu Muthana said the Army of Islam has been approached by Muslim leaders asking it to give more time to find a peaceful resolution. He said the group was considering the request.

Hamas sent out mixed messages late Monday. In Gaza, government spokesman Ghazi Hamad expressed hope for a diplomatic solution. But Osama Hamdan, one of the most senior members of the exiled Hamas leadership, ruled out a compromise and threatened to abduct more Israelis.

"If this operation does not lead to the release of prisoners now, let's postpone talk ... and we will continue resistance. Other (Israelis) might be taken prisoner," Hamdan, Hamas' representative in Lebanon, told Al Manar television.

In the West Bank city of Ramallah early Tuesday, after surrounding a Palestinian police building, Israeli forces arrested three militants said to be involved in the abduction and killing of an 18-year-old Israeli settler last week. The military said a fourth was arrested earlier.

The kidnapping of the teen, Eliahu Asheri, added tension to the situation surrounding the capture of the soldier. Asheri's body was found Thursday near Ramallah.

In the hours before the deadline expired, Israel kept up its pressure on Hamas with airstrikes.

Early Tuesday, Israeli aircraft hit the student council building at the Islamic University in Gaza City, witnesses said, badly damaging it. No one was hurt. The university is a Hamas stronghold. The military said it hit a "compound used by terror groups for instructing and directing terrorists."

The military said it also hit another Hamas facility in northern Gaza.

In addition, Palestinian residents said several Israeli tanks and a bulldozer entered the northern Gaza town of Beit Hanoun after midnight. The military said they were still outside. Israel has been building up troops across from northern Gaza, preparing for an invasion.

A Hamas militant was killed and four wounded in an Israeli airstrike in Beit Hanoun just after midnight, Palestinians said. Israel said its air force targeted Palestinians planting a bomb near soldiers' positions.

The White House and European Union have urged the militants to release Shalit, while also calling on Israel to show restraint.

"It is the responsibility of Hamas to return the Israeli soldier. That's how all this got started. We have also been encouraging Israel from the very beginning to practice restraint and continue to do so," White House press secretary Tony Snow said.

Switzerland offered more forceful criticism, accusing Israel of violating international law in its Gaza offensive by inflicting heavy destruction and endangering civilians in acts of collective punishment banned under the Geneva Conventions.

Many Palestinians say they do not wish Shalit to be harmed, but they back the demand to free some of the 9,000 Palestinian prisoners held by Israel.

"I think they should release the women and children and (the militants should) release the soldier. But without anything in return, they'll kill him," said Saked Abu Kosh, a 30-year-old pharmacist in the southern town of Rafah.