The developments in the seven-month-old war came on Monday as Israeli forces struck Rafah on Gaza's southern edge from the air and ground and ordered residents to leave parts of the city, which has been a refuge for more than a million displaced Palestinians.
Hamas said in a brief statement that its chief, Ismail Haniyeh, had informed Qatari and Egyptian mediators that the group accepted their proposal for a ceasefire.
Israeli Prime Minister Benjamin Netanyahu's office said later that Hamas' latest truce proposal falls short of Israel's demands but Israel would send a delegation to meet with negotiators to try to reach an agreement.
In a statement, Netanyahu's office added that his war cabinet approved continuing an operation in Rafah.
"The war cabinet unanimously decided that Israel continue the operation in Rafah to exert military pressure on Hamas in order to advance the release of our hostages and the other goals of the war," the statement said.
Benjamin Netanyahu's office says a delegation will meet negotiators to try to reach an agreement. (AP PHOTO)
United Nations Secretary-General Antonio Guterres urged Israel and Hamas "to go the extra mile needed to make an agreement", his spokesman said.
A US official familiar with truce negotiations told Reuters that Netanyahu and the war cabinet "have not appeared to approach the latest phase of negotiations in good faith".
US State Department spokesman Matthew Miller said Washington would discuss the Hamas response with its allies in the coming hours, and a deal was "absolutely achievable".
"We want to get these hostages out, we want to get a ceasefire in place for six weeks, we want to increase humanitarian assistance," White House national security spokesperson John Kirby said, adding that reaching an agreement would be the "absolute best outcome".
More than 34,600 Palestinians have been killed in the conflict, according to Gaza health officials. The UN has said famine is imminent in the enclave.
The war began when Hamas militants attacked Israel on October 7, killing about 1200 people and abducting 252 others, of whom 133 are believed to remain in captivity in Gaza, according to Israeli tallies.
Any truce would be the first pause in fighting since a week-long ceasefire in November, during which Hamas freed around half of the hostages.
Since then, all efforts to reach a new truce have foundered over Hamas' refusal to free more hostages without a promise of a permanent end to the conflict, and Israel's insistence that it would discuss only a temporary pause.
Earlier on Monday, Israel ordered the evacuation of parts of Rafah, the city on the Egyptian bordered that has served as the last sanctuary for around half of Gaza's 2.3 million residents.
Israel's closest ally, the United States, has called on it not to assault Rafah, saying it must not do so without a full plan in place to protect civilians there, which has yet to be presented. Washington is committed to stopping Israel's attack on Rafah, the US official said.
Israel said on Monday it was conducting limited operations on the eastern part of Rafah. The was being accompanied by massive air strikes, according to Palestinian residents.
"They have been firing since last night and today after the evacuation orders, the bombardment became more intense because they want to frighten us to leave," Jaber Abu Nazly, a 40-year-old father of two, told Reuters via a chat app.
"Others are wondering whether there is any place safe in the whole of Gaza," he added.
