US Secretary of State Antony Blinken was in Israel on Wednesday, where he was expected to press for what he called an "essential" truce agreement as the war with Hamas entered its fifth month.
The diplomat was due to meet Israel's leaders as part of a Middle East crisis tour after earlier stops in Saudi Arabia, Egypt and Qatar.
Qatar, which mediated a temporary ceasefire earlier in the conflict, said Hamas had given a response to a new proposed deal to pause the fighting.
"The reply includes some comments, but in general it is positive," Qatari Prime Minister Mohammed bin Abdulrahman Al-Thani said after meeting Blinken in Doha.
Blinken said Hamas's reply had been "shared" with Israel and he would discuss it there on Wednesday.
He also said there was still "a lot of work to be done" but that he believed "that an agreement is possible and indeed essential".
Israel's spy agency Mossad also received the Hamas response, Prime Minister Benjamin Netanyahu's office said, and "its details are being thoroughly evaluated".
Netanyahu, who has yet to comment directly on the response, said on Tuesday: "We are on the way to the total victory and we will not stop."
Pressure for a ceasefire has mounted as Israeli forces push towards the town of Rafah on Gaza's southern border with Egypt, where more than half the besieged territory's population has taken shelter.
"To be clear, intensified hostilities in Rafah in this situation could lead to large-scale loss of civilian lives, and we must do everything possible within our power to avoid that," said Jens Laerke, spokesperson for the UN aid coordination office OCHA.
The war started with Hamas's unprecedented attacks on Israel on October 7, which killed about 1,160 people, mostly civilians, according to an AFP tally based on official Israeli figures.
Militants also seized around 250 hostages, with Israel saying 132 remain in Gaza.
Vowing to eliminate Hamas, Israel has launched air strikes and a land offensive that have killed at least 27,585 people in Gaza, mostly women and children, according to the health ministry in the Hamas-run territory.
The campaign has devastated swathes of Gaza, destroyed hospitals and displaced more than half of its population of 2.4 million, while food, water, fuel and medicine are in dire shortage.
"The humanitarian situation in the Gaza Strip is beyond catastrophic," said Tommaso Della Longa, spokesman for the International Federation of Red Cross and Red Crescent Societies.
Israeli troops, with air and naval support, have been engaged in heavy combat centred on Gaza's main southern city of Khan Yunis, the hometown of Hamas's Gaza chief, Yahya Sinwar, accused by Israel of masterminding the October 7 attack.
Around 8,000 displaced people had been evacuated from the besieged Al-Amal hospital in Khan Yunis, where they had sought refuge, after weeks of heavy shelling and fighting nearby, according to the Red Cross.
Gaza's health ministry said at least 100 people were killed overnight Tuesday to Wednesday.
Israel has warned it could also push on into Rafah, the last place of refuge for many Palestinians fleeing the fighting.
The army "will reach places where we have not yet fought... right up to the last Hamas bastion, which is Rafah", Israeli Defence Minister Yoav Gallant said earlier this week.
Safia Marouf, sheltering in Rafah with her family after being uprooted from their home further north, said she is afraid of what is to come.
"The children are scared all the time, and if we want to leave Rafah, we don't know where to go. What will be our destiny and that of our children?"
Last week, a Hamas source said the proposed truce calls for a six-week pause to fighting for a hostage-prisoner exchange, as well as more aid for Gaza.
On Monday, Netanyahu said Hamas had presented "demands that we will not accept" for an exchange involving thousands of prisoners.
The Israeli leader is under pressure to end the war and bring the hostages home, amid divisions within his cabinet and public fury over the fate of the remaining captives.
The United States has strongly backed Israel with munitions and diplomatic support but also urged steps to reduce civilian casualties.
On his latest diplomatic tour to the region, Blinken first stopped in Saudi Arabia, which Washington has been pushing to normalise ties with Israel.
After comments from Washington indicated "positive feedback" on establishing ties, the kingdom emphasised it would not be willing to do so without recognition for an independent Palestinian state.
"The Kingdom has communicated its firm position to the US administration that there will be no diplomatic relations with Israel unless an independent Palestinian state is recognised on the 1967 borders with East Jerusalem as its capital," the Saudi foreign ministry said in a statement Wednesday.
Violence has also flared in Lebanon, Iraq, Syria and Yemen, where Iran-backed groups have launched attacks in support of Hamas, triggering counterattacks by Israel, the United States and its partners.
Israeli strikes on the Syrian city of Homs killed five people, including three civilians, on Wednesday, a war monitor said.
Its fighter jets had also targeted bases of the Iran-backed Hezbollah movement near Marwahin and Meiss El Jabal in southern Lebanon.
Yemen's Iran-backed Huthis have meanwhile for weeks been targeting what they say are Israel-linked ships in the Red Sea and Gulf of Aden in solidarity with Palestinians.
The attacks have disrupted global trade and prompted reprisals by US and British forces.
