Mediators to the Gaza War cease-fire talks said Friday the two-day talks wrapped up and they aim to reconvene in Cairo next week to seal a deal to stop the fighting, writes PBS NEWS.

In a statement Friday, the United States, Egypt and Qatar said talks were constructive and conducted in a positive atmosphere. They presented both parties with a proposal and hope to continue working on the details of the implementation in the coming days.

The new round of talks began Thursday and were aimed at halting the 10-month war and securing the release of scores of hostages, with a potential deal seen as the best hope of heading off an even larger regional conflict. Hamas, which didn’t participate directly in the talks, accuses Israel of adding new demands to a previous proposal that had U.S. and international support and to which Hamas had agreed in principle.

Both sides have agreed in principle to the plan President Joe Biden announced on May 31. But Hamas has proposed amendments and Israel has suggested clarifications, leading each side to accuse the other of trying to tank a deal.

Hamas has rejected Israel’s demands, which include a lasting military presence along the border with Egypt and a line bisecting Gaza where it would search Palestinians returning to their homes to root out militants.

On Friday mediators said it presented a bridging proposal to both parties consistent with the plan laid out by Biden. This proposal builds on areas of agreement and bridges remaining gaps, that allow for a swift implementation of the deal.

The new push for an end to the Israel-Hamas war came as the Palestinian death toll in Gaza climbed past 40,000, according to Gaza health authorities, and fears remained high that Iran and Hezbollah militants in Lebanon would attack Israel in retaliation for the killings of top militant leaders.

International mediators believe the best hope for calming tensions would be a deal between Israel and Hamas to halt the fighting and secure the release of Israeli hostages. International diplomacy to prevent the war in Gaza from spreading into a wider regional conflict intensified Friday, with the British and French foreign ministers making a joint trip to Israel.

White House National Security spokesperson John Kirby called the talks an important step. He said a lot of work remains given the complexity of the agreement and that negotiators were focusing on its implementation.