Shalit was seized by Palestinian militants in a cross-border raid over two years ago.
The hard-line Islamic group wants Israel to release in exchange for Shalit 450 Palestinians jailed on terrorist charges, as well as 550 other prisoners, including women, teenagers, and Hamas ministers and parliamentarians.
"The majority of these people do not belong to Hamas, but this may be a real chance for them to obtain freedom," Hamas spokesman Fawzi Barhoum said.
Hundreds of Israelis demanding the immediate release of Shalit attempted to block the delivery of aid to the Gaza Strip on Sunday. Barhoum advised the protesters to "put pressure on their own government" to accept Palestinian terms.
Barhoum also said Hamas would prolong the current six-month ceasefire agreement with Israel, due to expire in November, only after Tel Aviv lifted a blockade of the enclave, home to 1.5 million people.
Over 11,000 Palestinians are imprisoned in Israeli jails.
