But Prime Minister Benjamin Netanyahu warned he would not pay "any price" for the release of Sgt Shalit, seized by militants on the Gaza border in 2006.
Talks to free Sgt Shalit broke down last year, after representatives of Israel and Hamas, which controls Gaza, failed to agree on a list of prisoners.
Hamas wants militants freed who Israel says have "blood on their hands".
On Sunday, Sgt Shalit's family began an 11-day cross-country march to the prime minister's office in Jerusalem, where they say they plan to camp until he comes home.
In a televised address, Mr Netanyahu said the people of Israel were united in their desire to bring the captured soldier home, but that the nation could not pay any price because experience showed that many Palestinian militants released before had returned to violence.
"The most famous case is the 'Jibril Deal', in which 1,150 were released. Almost half went back to terrorism," he said.
Mr Netanyahu then alleged that those released under the 1983 agreement - including Ahmed Yassin, who went on to found Hamas - "went back to murdering hundreds of Israelis and constituted the hard-core of the second Intifada".
"In the deal presented by the German mediator, to which I agreed, there were 1,000 terrorists - that's the price I am willing to face to bring Shalit home," he added.
Mr Netanyahu said the offer from December was "ready for immediate implementation", and no response had been received from Hamas.
"But there are prices that I am not prepared to pay and they are not included in this difficult deal," he added.
"I stick to two principles - the terrorists must not return to Judea and Samaria [the West Bank], and no arch-terrorists will be released."
Israeli media said Hamas quickly dismissed Mr Netanyahu's offer.
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