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.
Hamas confirmed it delivered its response to proposals hammered out a week ago in Paris between Qatar and other mediators.
Blinken said Hamas's reply had been "shared" with Israel and he would discuss it there on Wednesday.
Antony Blinken meets with Qatar's Emir Sheikh Tamim Bin Hamad Al Thani in Doha on Tuesday. Reuters
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.
Agence France-Presse