This would be followed by "immediate negotiations" for a permanent peace deal, including a guarantee of no more "war and aggression", Hamas claimed.
Details are currently sparse, but the last proposal fell through due to Hamas making demands on Israel deemed unreasonable and unworkable.
Both Israeli and US representatives withdrew from Doha several weeks ago, accusing the terror group of refusing to act "in good faith".
Egypt is said to have played a leading role in producing the new proposal, which must now be put to Israel. Previously, Qatar and the US were more dominant in the mediation process.
However, it is unclear whether Israel is still ready for a two-phased deal, with Prime Minister Netanyahu noting: "We can see clearly that Hamas is under immense pressure."
And a government official reportedly indicated to the Times of Israel that Jerusalem remains committed to a comprehensive deal, including the release of all hostages in one phase, Hamas' disarmament and surrender, and the demilitarisation of Gaza.
"Israel’s position has not changed — [regarding both] the release of all the hostages and adherence to the other conditions defined for ending the war," they said.
No official response to the proposal has yet been provided by Israel, but one is expected to be sent by the end of the week.
A total of 50 hostages remain in Hamas captivity, only 20 of whom are believed to be alive.
