Israel said the terms of a ceasefire deal Hamas accepted on Monday remained "far from" meeting its demands and warned its military operations in Rafah would continue, even as it sent negotiators to talk to mediators.

In a statement Monday, Hamas said the head of its political bureau, Ismail Haniyeh, told the Qatari prime minister and Egyptian intelligence minister that the militant group had accepted their proposals for a ceasefire and hostage deal.

Shortly afterwards, Israel said the proposal Hamas had accepted was still far from the "necessary requirements," but that it would send a delegation to the mediators. It also reiterated its commitment to an offensive in the southern Gaza city of Rafah, saying its war cabinet had "unanimously decided" to continue with the operation "to exert military pressure on Hamas."

Prior to Israel鈥檚 response, Palestinians had been celebrating in the streets over Hamas鈥 announcements. In Tel Aviv, hostage families and their supporters implored Israel鈥檚 leaders to accept the deal.

But later on Monday evening, the Israel Defense Forces said that it is 鈥渃urrently conducting targeted strikes against Hamas terror targets in eastern Rafah in the southern Gaza Strip.鈥

CNN political and global affairs analyst Barak Ravid said Israeli forces were going to take over the Palestinian side of the Rafah crossing in the next few hours, citing two sources with direct knowledge.

The news comes just hours after Israel ordered Palestinians living in Rafah, a city in southern Gaza, to 鈥渆vacuate immediately.鈥

The order raised fears that Israel鈥檚 long-threatened assault on the city could be imminent. More than 1 million Palestinians have fled to Rafah, where Hamas is believed to have regrouped after Israel鈥檚 destruction of much of the north of Gaza.

A source familiar with Israeli plans told CNN that a limited incursion into Rafah was intended to keep pressure on Hamas to agree a deal that would bring about a ceasefire and a hostage release.

Israel news

No agreement

The details of the proposals Hamas says it has agreed to remain unclear, and whether it is referring to the most recent ceasefire proposal, as outlined last week, or a revised version of it.

A senior Israeli and a senior US official said that Hamas had agreed to a framework proposal, which diverges from the one Israel had helped craft with Egypt. The latest proposal calls for an end to the war, which Israeli Prime Minister Benjamin Netanyahu has previously said he will not accept, the senior American official said.

According to a press release, Hamas said it would not back down from its demands in the latest proposal, which include a 鈥渃easefire, complete withdrawal, dignified exchange, reconstruction, and lifting of the blockade.鈥

Benny Gantz, a member of Israel鈥檚 war cabinet, said Monday there were 鈥渟ignificant gaps鈥 between Israel and Hamas. 鈥淒espite this, we continue to turn over every stone and a delegation will go to Cairo.鈥

A previous framework, which Israel helped craft but had not fully agreed to, called for the release of between 20 and 33 hostages over several weeks in exchange for a temporary ceasefire and the release of Palestinian prisoners.

After the initial exchange, according to that framework, there would follow what sources describe as the 鈥渞estoration of sustainable calm鈥 during which the remaining hostages, captive Israeli soldiers and the bodies of hostages would be exchanged for more Palestinian prisoners.

The White House on Monday confirmed that there had 鈥渂een a response from Hamas鈥 to a proposed hostage deal in Israel, and that U.S. President Joe Biden had been briefed on that response, but otherwise declined to weigh in specifically on what a deal could entail.

Biden is 鈥渁ware of where the situation and where the process is,鈥 White House national security spokesman John Kirby told a press briefing. CIA Director Bill Burns remains in the region 鈥渨orking in real time on the ground,鈥 Kirby added.

鈥淲e still believe that reaching an agreement is the absolute best outcome not only for the hostages, but for the Palestinian people and we鈥檙e not going to stop working to that outcome,鈥 he said.

IDF operations ongoing

Asked whether Hamas鈥 acceptance of a deal could change Israel鈥檚 plans for Rafah, Israel Defense Forces (IDF) spokesperson Daniel Hagari said the military would continue to operate in Gaza. He said operations are ongoing, but that the IDF is making every effort in the negotiations to bring the hostages home as 鈥渇ast as possible.鈥

Netanyahu has come under fierce pressure from the more extreme wing of his coalition not to accept the ceasefire proposal outlined last week, and to focus instead on destroying Hamas in Rafah.

Orit Strook, Israel鈥檚 settlements minister and a member of the far-right Religious Zionism party, said last week that accepting the deal would 鈥渢hrow鈥 Israel鈥檚 military progress 鈥渋n the trash.鈥

Itamar Ben Gvir, Israel鈥檚 national security minister, said Netanyahu had 鈥減romised that Israel would enter Rafah, assured that the war would not end, and pledged that there would be no reckless deal.鈥

But large parts of the Israeli public have demanded Netanyahu accept a deal. Families and supporters of the hostages blocked the Ayalon Highway in Tel Aviv last week, holding a banner reading: 鈥淩afah or the hostages 鈥 choose life.鈥

Benny Gantz, a member of Israel鈥檚 war cabinet but seen as a rival and possible successor to Netanyahu, said the return of hostages was more urgent that entering Rafah.

Responding to Monday鈥檚 announcement by Hamas, the Hostages Families Forum said: 鈥淣ow is the time for all that are involved, to fulfil their commitment and turn this opportunity into a deal for the return of all the hostages.鈥

This is a developing story and will be updated.