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Steve Witkoff, US special envoy for the Middle East, said on Wednesday that the US is finalising a written agreement that may form the basis for a Gaza ceasefire deal.
Standing beside President Donald Trump at the White House, Mr Witkoff said he was optimistic that the terms of a deal would lead to a resolution.
“We are on the precipice of sending out a new term sheet that hopefully will be delivered later on today,” Mr Witkoff said.
“The President is going to review it. And I have some very good feelings about getting to a long-term resolution, temporary ceasefire and a long-term resolution, a peaceful resolution of that conflict.”
Hamas said it has reached an agreement with Mr Witkoff on a “general framework” for a permanent ceasefire in Gaza, and that they were now awaiting a response from Israel.
In the statement, the group said the agreement includes the release of 10 Israeli hostages and several bodies, in exchange for a group of Palestinian prisoners.
The development comes amid renewed pressure on Israel to end its military campaign on Gaza, and allow food and humanitarian aid into the strip.
Mr Trump said the US is working to get more food to Palestinians in the Gaza Strip, where a US-backed non-governmental group called the Gaza Humanitarian Foundation started to deliver food this week.
“We're dealing with the whole situation in Gaza. We're getting food to the people of Gaza. It's been a very nasty situation, very nasty fight,” Mr Trump told reporters in the Oval office.
Israel blocked the entry of all deliveries of food and assistance after a fragile ceasefire collapsed in March, leading to widespread hunger and concerns of a looming famine.
On Tuesday, gunfire rang out as a crowd after Palestinians who had been queuing for food aid overran a distribution centre.
It was not clear if Israeli forces, private contractors or others had opened fire. Gaza's Health Ministry said at least one Palestinian was killed and 48 were wounded.
The UN and other aid groups who have been operating in Gaza have denounced the Gaza Humanitarian Foundation and refused to collaborate with it.
They say the use of armed contractors contravenes norms surrounding the delivery of humanitarian assistance to civilians during conflict.
The war began on October 7, 2023, after a Hamas attack killed about 1,200 people.
More than 54,000 Palestinians have been killed in Israeli strikes on the territory since, and much of the coastal enclave has been reduced to rubble.
