Israeli intelligence believes kidnapped soldier Gilad Shalit, 19, is being held a Palestinian refugee camp in the Rafah area, Israel Radio reported.
A senior intelligence officer told a parliament committee Israeli Defense Forces are trying to keep Shalit from being moved out of Gaza into Sinai.
A leader of the Hamas Islamic group said Tuesday that he believes Israel will give in to the demands of Palestinian militants who kidnapped an Israeli soldier.
"They are going to surrender, they are going to give in," Palestinian lawmaker Yehieh Mussa said in an interview with a Web site affiliated with Hamas.
But with troops poised to invade Gaza, Prime Minister Ehud Olmert on Monday ruled out bargaining with the captors and promised a "broad and ongoing" military offensive.
Israel feels that it cannot wait too long, reports CBS News correspondent Robert Berger. If it does, it would appear weak and its threats of a crushing military response would have no credibility.
However, large-scale army action appeared unlikely. Officials said they were pursuing a diplomatic solution and conceded that a broad attack would threaten the life of Shalit.
After more than 24 hours of silence, the militants claiming to hold Shalit issued their first demands Monday. The groups, linked to the Hamas-led Palestinian government, said Israel should release all imprisoned Palestinian women and children under 18 in return for information about Shalit.
Olmert rejected the demand. Addressing Jewish leaders in Jerusalem, he charged that the Palestinian attack on an army post at a Gaza crossing and the abduction of the soldier were part of a "murderous, hateful, fanatical Islamic extremist desire to destroy the state of Israel."
"This is not a matter of negotiations, this is not a matter of bargaining," he declared. "Release of prisoners is absolutely not on the agenda of the Israeli government."
Shalit was seized at a military post near the Gaza border by militants who infiltrated Israel through a tunnel. The attack was the first successful infiltration by militants since Israel withdrew from Gaza in September and immediately threatened to plunge the region into a major flare-up of violence.
Meanwhile, Israeli police on Tuesday said they are taking "very seriously" reports that a Jewish settler was abducted by Palestinian militants in the West Bank.
Israel Radio quoted relatives of the man as saying he did not return home on Monday night. The report said the man had been hitchhiking, which is common in Israel.
A spokesman for the Popular Resistance Committees — the same group that says it is holding Shalit — claimed his group had abducted the settler.
A spokesman for the Hamas-led government said Tuesday that he feels for the Israeli soldier kidnapped by Palestinian militants and wants him protected.
In interviews on Israeli media, Hamas has tried to calm tempers and dissuade Israel from carrying out a broad offensive in the Gaza Strip.
"First of all, I'm human and I feel like his mother and his father do and I know what it's like to be a prisoner," Ghazi Hamad told Israel's Army Radio in Hebrew, which he learned while serving five years in Israeli jails. "You want to protect the soldier and we are also interested in such a thing and we ... don't want to reach a situation of bloodshed, here or there."
Hamad said Monday that Shalit was alive and urged his captors to keep him safe. Israel believes the Hamas military wing was involved in the kidnapping and that the group's leader, Palestinian Prime Minister Ismail Haniyeh, is trying to get the militants to release him.
Shalit's family has been told that the soldier has a broken hand and a stomach wound. The message was passed to Israel by Palestinian President Mahmoud Abbas, who also said Shalit was being treated for the injuries.
The Jerusalem Post reports the intelligence officer who briefed Israeli legislators also told them the Kerem Shalom attack at which Shalit was kidnapped was being planned for almost two months.
With Israeli troops deployed along the border with Gaza, Egypt has deployed about 2,500 troops along its border with Gaza, concerned that Palestinians might attempt to cross into Egypt if Israel invades Gaza.
Army Radio reported that Olmert and his advisers decided not to stop supplies from entering the Gaza Strip, after initially considering whether to cut off water and electricity from the area if the soldier was not released within 48 hours.
Although Israel frequently carries out air raids in Gaza, ground troops have entered the area only three times — all briefly — since last year's pullout.
However, the officials said a limited operation could begin in the coming days. Such operations could include a rescue attempt or a limited mission meant to pressure Hamas to free the soldier.
The abduction delivered a blow to Abbas' efforts to coax Hamas into accepting a plan implicitly recognizing Israel. Abbas, elected separately last year, has endorsed the plan in hopes of lifting economic sanctions against Hamas and opening the way for new peace talks.
The crisis also exposed divisions within Hamas' ranks. The group maintains separate political and military wings, and political leaders based in Syria are more extreme than many leaders in the West Bank and Gaza.
In a closed briefing to lawmakers, Brig. Gen. Yossi Beidatz, a top Israeli intelligence official, said Hamas' leaders were divided about what to do with the soldier, participants said. He said the more moderate elements, including Haniyeh, consider the soldier a "hot potato" they should get rid of quickly.
Hamad said talk of a split in Hamas was "a big lie." However, he said the political leadership in Gaza, including Haniyeh, was not warned of the assault plans beforehand.
The statement demanding the inmates' release — about 500 people in all — was signed by Hamas' military wing and two offshoots of the small Popular Resistance Committees, which has strong links to Hamas. It offered information about Shalit but no guarantees of his safe return.
Palestinian militants previously have tried to use captured soldiers to win prisoners' releases, though Israel rarely has caved in. Israel now holds an estimated 8,000 Palestinians, many of them Hamas militants.
In Gaza City and the West Bank town of Ramallah, dozens of relatives of Palestinians held in Israeli prisons urged militants to hold Shalit until Israel agreed to a large-scale release.
"Kidnap a soldier and free 100 in return!" the crowd said. "Twist the Zionists' arms! Hope they can learn!"