Sources close to the talks told Reuters that Hamas hoped to build support among mediators for its offer, adding the group might agree to a five to seven-year truce in return for ending the war, allowing for the rebuilding of the Gaza Strip, the freeing of Palestinians jailed by Israel and the release of all hostages.
"The idea of a truce or its duration is not rejected by us and we are ready to discuss it within the framework of negotiations. We are open to any serious proposals to end the war," said Taher al-Nono, the media adviser for the Hamas leadership, in the first clear signal that the group was open to a longer-term truce.
However, Nono ruled out a core Israeli demand that Hamas lay down its arms.
Israel wants to see the Gaza Strip demilitarised.
"The weapon of resistance is not negotiable and will remain in our hands as long as the occupation exists," Nono said.
Hamas' founding charter calls for Israel's destruction but it has signalled in the past that it might agree to a long-term truce in return for ending Israeli occupation.
Israel's Deputy Foreign Minister Sharren Haskel downplayed chances this week for the new proposal to lead to a breakthrough unless Israel's core demands were met.
"The war could end tomorrow if Hamas released the remaining 59 hostages and laid down its weapons," Haskel said in Jerusalem on Tuesday.
Israel resumed its offensive in the Gaza Strip on March 18 after a January ceasefire collapsed, saying it would keep up pressure on Hamas until it frees the remaining hostages still held in the enclave.
Up to 24 of them are believed to still be alive.
Israel has blocked all aid into the enclave and hundreds of thousands have been displaced as its forces have seized territories it has designated as a buffer zone.
More than 2000 Palestinians, many of them civilians, have been killed in Israeli strikes since, according to health authorities.
The war was triggered by Hamas' October 7 2023 attack which killed 1200 people and involved the taking of 251 hostages to the Gaza Strip.
Since then, more than 51,400 Palestinians have been killed in the Israeli offensive in the strip, according to local health officials.