Mark Regev, an Israeli foreign ministry spokesman, said on Saturday: "Prime Minister Ehud Olmert has reiterated that there will be no deals, that either Shalit will be released or we will act to bring about his release."
Also on Saturday, George Bush, the US president, said freeing the Israeli soldier was crucial to ending the crisis in Gaza and should be the initial goal.
The Popular Resistance Committees (PRC) group said in a statement that they were seeking the release of "1,000 Palestinian, Arab, Muslim and other prisoners".
"We are declaring to the public our just and humanitarian demands," the group said.
The PRC has said it carried out Sunday's attack on an Israeli army post during which 19-year-old corporal Gilad Shalit was captured.
Israeli police have denied claims by the Al-Aqsa Martyrs' Brigades group that a second Israeli soldier had been seized.
Ziad Abu Ein, an official with the Fatah movement, said mediators involved in efforts to release the soldier had reported he was fine.
"He is in a stable condition according to mediators," Abu Ein told a news conference in the West Bank city of Ram Allah.
"He was treated by a Palestinian doctor. He is fine now."
Early on Saturday, Israel fired missiles at what it said were training camps for Palestinian fighters in Gaza.
Many parts of Gaza, already facing a worsening humanitarian crisis because of a cut in Western aid since Hamas took office, are now without electricity and water because of the Israeli strikes.
Bush: Release soldier first
Bush, in a telephone conversation initiated by Tayyip Erdogan, the Turkish prime minister, said "the initial goal should be freeing the Israeli soldier. That is the key to ending the crisis", White House National Security Council spokesman Frederick Jones said.
The United States has privately urged Israel to be careful over its military action, worried that tough moves in Gaza will boost Palestinian support for Hamas and further escalate tensions.
The regional fallout from the escalation in violence also deepened with the US saying Syria was partially responsible for the crisis.
The UN Security Council debated the crisis on Friday, with Israeli and Palestinian representatives and their allies trading criticisms.
John Bolton, the US ambassador to the UN, said: "We would not be where we are right now if it were not for Syria's support and harbouring of terrorists."
Bolton demanded Syria turn over Khalid Mishaal, Hamas's exiled political leader who lives in Damascus, for prosecution.
"In addition, we call upon Syria to stop financing the terrorists and stop co-operating with other states, such as Iran, which finance terrorists," Bolton said.
Ismail Haniya, the Palestinian prime minister, said on Friday: "We are working to end this crisis, but the aggression must stop and the siege has to be lifted."