Hamas says it has informed Qatari and Egyptian mediators that it has accepted their proposal for a new Gaza ceasefire and hostage release deal with Israel.
"The ball is now in Israel's court," an official in the Palestinian group said.
Israeli Prime Minister Benjamin Netanyahu said Hamas' proposal was "far from Israel's basic requirements", but negotiators would continue discussions.
The basis of the deal is a weeks-long pause in fighting and the release of several dozen hostages held by Hamas.
Hamas's announcement came hours after the Israeli military told Palestinians to evacuate eastern parts of Rafah, as it appeared to be preparing for a long-threatened assault on Hamas hold-outs in the southern Gaza city.
Tens of thousands of residents are believed to be affected by the operation and many were seen cramming into vehicles or onto donkey carts on Monday.
A Hamas official called the evacuation order, which was followed by Israeli air strikes, a "dangerous escalation".
On Monday evening, Hamas put out a statement saying its political leader, Ismail Haniyeh, had informed Qatar's prime minister and Egypt's intelligence chief of its "approval of their proposal regarding a ceasefire agreement".
A senior Palestinian official familiar with the proposal told the OceanNewsUK that Hamas had agreed to end "hostile activity forever" if the conditions were met.
That phrase hinted that Hamas might be contemplating the end of its armed struggle, although no further details were provided. It would come at the conclusion of a two-phase ceasefire deal, with each phase lasting 42 days.
The first phase would include the release of the female Israeli soldiers being held hostage, each in exchange for 50 Palestinian prisoners in Israeli jails, including some who are serving life sentences.
During this period, Israeli troops would remain within Gaza. But within 11 days of the ceasefire coming into force, Israel would begin dismantling its military facilities in the centre of the territory and would withdraw from Salah al-Din Road, which is the main north-south route, and the coastal road.
After 11 days, displaced Palestinians would be allowed to return to the north.
The second phase would conclude with a "sustainable long period of calm" and the complete lifting of the blockade of Gaza, according to the official.
"The ball is now in the court of [Israel], whether it will agree to the ceasefire agreement or obstruct it," a senior Hamas official told AFP news agency.
The were celebrations in Gaza as news of the Hamas statement spread.
But an unnamed Israeli official swiftly told Reuters news agency that the proposal Hamas had accepted was a "softened" version of an Egyptian proposal which included "far-reaching" conclusions that Israel could not accept.
"This would appear to be a ruse intended to make Israel look like the side refusing a deal," the official said.
Later, Prime Minister Netanyahu's office said in a statement: "Even though the Hamas proposal is far from Israel's basic requirements, Israel will send a delegation of mediators to exhaust the possibility of reaching an agreement under conditions acceptable to Israel."
At the same time, Israel's war cabinet had decided to continue the Rafah operation "to exert military pressure on Hamas to advance our war aims: the release of our hostages, destroy Hamas's military and governing capabilities and ensure that Gaza does not pose a threat to Israel in the future", it added.
The statement came at the same time as the Israeli military announced it was striking Hamas targets in eastern Rafah.
US state department spokesman Matthew Miller told reporters that the US - which is attempting to broker a deal along with Qatar and Egypt - was reviewing Hamas's response and "discussing it with our partners".
"We continue to believe that a hostage deal is in the best interests of the Israeli people. It's in the best interests of the Palestinian people," he added.
"It would bring an immediate ceasefire. It would allow increased movement of humanitarian assistance and so we're going to continue to work to try to reach one."
The war began when Hamas gunmen stormed into southern Israel on 7 October, killing about 1,200 people and seizing more than 250 hostages.
More than 34,700 people have been killed in Gaza during the ensuing Israeli military campaign, according to the territory's Hamas-run health ministry.
A deal agreed in November saw Hamas release 105 hostages in return for a week-long ceasefire and some 240 Palestinian prisoners in Israeli jails.
Israel says 128 hostages remain unaccounted for in Gaza, at least 34 of whom are presumed dead.
