GAZA CITY, Gaza Strip (AP) – Militants gave Israel 24 hours starting Monday to begin releasing hundreds of Palestinian prisoners, implying they would kill an abducted Israeli soldier if their demands were not met.

Israeli Prime Minister Ehud Olmert rejected any negotiations with the militants, and the army pressed ahead with its Gaza offensive. Privately, though, some officials said the government had not ruled out any options to win Cpl. Gilad Shalit’s freedom.

Israel has pounded Gaza with airstrikes and artillery shells for nearly a week in an unsuccessful effort to force the Hamas-linked militants to release Shalit. It has been building up troops across from northern Gaza, preparing for an invasion. Tanks and troops moved in and out throughout the day and the military said it was carrying out “limited” operations to uncover explosives and tunnels.

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

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.”

In the West Bank city of Ramallah, Israeli forces surrounded a building early Tuesday. The military said militants who abducted and killed an 18-year-old Israeli settler earlier this week were holed up inside, and the goal was to arrest them.

After Shalit was seized in a June 25 raid on an army post that left two comrades dead, his captors demanded Israel free all imprisoned Palestinian women and minors in exchange for information about him. They later increased their demand to include the release of 1,000 more prisoners.

Early Monday, Hamas’ military wing – one of the three groups holding Shalit – issued a statement giving Israel until 6 a.m. Tuesday (11 p.m. EDT Monday) to start freeing the prisoners. The other two groups are also Hamas-linked.

If Israel does not comply, “we will consider the soldier’s case to be closed,” the statement said, “and then the enemy must bear all the consequences of the future results.”

Abu Obeida, spokesman for the Hamas military wing, later told The Associated Press that Israel must at least begin freeing the women and minors.

“Israel must understand that the resistance factions are serious in this matter. They will close this case if (Israel) doesn’t deal with the demands,” he said, adding that the militants would not compromise.

With the deadline less than eight hours away, Hamas sent out mixed messages late Monday. Ghazi Hamad, spokesman for the Hamas-led government, expressed hope for a diplomatic solution. But Osama Hamdan, Hamas’ representative in Lebanon and one of the most senior members of the exiled 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 told Al Manar television.

Abu Obeida refused to specify what the militants would do if their ultimatum was ignored. Killing Shalit, however, would remove their only leverage against Israel and likely would invite far harsher reprisals against Gaza.

“If God forbid, they should hurt the soldier, our operations will be far, far worse,” Israeli Justice Minister Haim Ramon warned.

Olmert said the government would not cave in to extortion.

“There will be no negotiations to release prisoners,” his office said, adding that he holds the Hamas-led Palestinian Authority responsible for Shalit’s safety.

But government and military officials said privately that Israel would pursue all options to get Shalit back. Israel has released prisoners before in lopsided exchanges for captured citizens or the dead bodies of soldiers killed in battle.

Mohammed Dahlan, a Palestinian legislator and close ally to moderate President Mahmoud Abbas, said the ultimatum was a negotiating tactic and that efforts to broker a compromise were continuing.

The White House urged the militants to release Shalit.

“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.

In their statement, Shalit’s captors accused Israel of not “learning lessons” from the fate of other kidnapped soldiers. The last Israeli soldier kidnapped by Hamas, Nachshon Wachsman, died in 1994 in an Israeli commando raid on his captors’ Jerusalem hideout.

Wachsman’s mother, Esther, accused Israel’s leaders of a lack of candor in dealing with hostage cases.

“I am not calling for the release of murderers, but (Israel’s leaders) should not insult our intelligence because they have negotiated and they have given in to terror,” she wrote in the Haaretz newspaper.

Egypt has been trying to mediate the crisis, but its efforts have been complicated by confusion over who has the authority on the Palestinian side to make a deal. The Palestinian government says it had nothing to do with the abduction.

The Hamas-linked militants who seized Shalit are presumed to answer to the group’s leaders in Syria, but those in Damascus say they bear no responsibility for the soldier.

Egyptian President Hosni Mubarak met King Abdullah in Saudi Arabia on Monday in efforts to reach a deal over Shalit. Mubarak already has tried to enlist Syria’s help.

Turkish Prime Minister Tayyip Erdogan said he had sent a special envoy to Syria to discuss ways of solving the crisis with President Bashar Assad.

Israeli Defense Minister Amir Peretz warned Damascus that he held it responsible for Shalit’s fate because the Syrian government harbored Hamas’ leaders.

“I suggest that (Syrian President) Bashar Assad, who is trying to operate with his eyes shut tight, open his eyes, because he is responsible,” Peretz said.

Also Monday, Israel closed the Karni cargo crossing into Gaza, citing a security threat, just a day after Israel reopened it so badly needed humanitarian supplies could reach the coastal strip. The crossing is the main gateway for goods to enter Gaza.

Palestinian U.N. representative Riyad Mansour appealed to the Security Council to help avert a major crisis in the Middle East by compelling Israel to stop its offensive in Gaza. Arab nations at the U.N. held a closed-door meeting to debate whether to seek a Security Council resolution. They made no decision and decided to meet again Wednesday.

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