"The return of (Israeli) occupation prisoners has three prices. The first is the relief of our people and their return to a normal life. The second is ending the aggression, and the third is a real prisoner swap deal that frees our 10,000 prisoners in Israeli jails," Khalil al-Hayya, a member of the group's political bureau, said in an interview with Qatar-based Al Jazeera TV.
He said Israel refuses to withdraw from Gaza and rejects allowing displaced Palestinians to return to their homes.
On Saturday, Israeli Prime Minister Benjamin Netanyahu described Hamas’s proposal on the cease-fire and prisoner swap as "delusional."
"Netanyahu retreated last week what he had agreed to in the Paris paper," said al-Hayya.
On Feb. 7, Hamas proposed a three-stage plan for a Gaza cease-fire that includes a 135-day pause in the fighting in return for the release of hostages, according to a Palestinian source.
The original framework agreement was worked out during a Paris meeting last month of top officials from the US, Israel, Qatar and Egypt.
Israel believes there are 134 Israelis being held in Gaza after the Israeli army had managed last week to free two Israelis held in the city of Rafah in the southern Gaza Strip.
Israel has launched a deadly offensive on the Gaza Strip following an attack by Hamas on Oct. 7. The ensuing Israeli bombardment has killed nearly 29,092 and injured about 69,028 with mass destruction and shortages of necessities.
The Israeli war on Gaza has pushed 85% of the territory's population into internal displacement amid acute shortages of food, clean water and medicine, while 60% of the enclave's infrastructure has been damaged or destroyed, according to the UN.
Israel stands accused of genocide at the International Court of Justice. An interim ruling in January ordered Tel Aviv to stop genocidal acts and take measures to guarantee that humanitarian assistance is provided to civilians in Gaza.