U.S. Secretary of State Antony Blinken told reporters in Washington that the Biden administration is working "intensively" on a hostage deal, saying "We are working to bring the remaining hostages in Gaza, we are working intensively with Egypt and Qatar on a proposal to release them."

As part of an intensive push following what U.S. President Joe Biden said on Monday he hopes includes a six-week ceasefire to the war, William Burns, CIA Director, held talks in Cairo following a Paris meeting late last month with officials from Qatar, Egypt, and Israel.

Egypt and Qatar are mediating the deal, and according to the Egyptian Information Authority, President Abdel Fattah el-Sisi held talks with Burns and Qatari Prime Minister Sheikh Mohammed II, who also mediated an increase in humanitarian aid in Gaza and better protection for civilians.

In a statement on its website, it cited "keen interest in continuing consultation and coordination" on key issues, indicating gaps remain between the parties.

The Egyptian statement did not mention Israel, while a Reuters correspondent said the Israeli delegation left Cairo returning home, and the Prime Minister's office did not immediately respond to a request for comment.

But Egyptian media reported that the talks were positive.

According to Israeli media, "senior officials participating in the talks—Mossad Director David Barnea, Shin Bet Director Ron Ronen, and General Nitzan Alon—put forward a new proposal to advance the talks that were rejected by Prime Minister Benjamin Netanyahu."

Daniel Hagari, spokesman for the Israel Defense Forces, confirmed that Alon, who is considered pivotal in this process, did not go to the talks, but emphasized his ongoing involvement, and Ofir Falk, Netanyahu's foreign policy advisor, joined the delegation, according to Hebrew media reports.

A Palestinian official said earlier that the two sides were seeking a formula acceptable to Hamas, which "says that a deal can only be signed once it is based on an Israeli commitment to end its war and withdraw its forces from Gaza."

Israel rejected all calls to end the war without defeating Hamas and instead the Israel Defense Forces must retain security control in Gaza.

A Hamas official said the movement told participants it does not trust Israel not to renew the war if the hostages are released.

The talks to free the 134 remaining hostages occurred amid a sharp international outcry against a potential operation in Rafah and renewed push for a ceasefire and the start of a two-state process.

The threat of the looming Rafah operation has become one of the means of pressure used by mediators to push Hamas to soften some of its red lines.

King Abdullah of Jordan was in Washington, where he met with U.S. President Joe Biden at the White House on Monday, and with Vice President Kamala Harris as well as members of Congress on Tuesday, emphasizing the need for an immediate ceasefire in Gaza.

In Berlin, German Foreign Minister Annalena Baerbock, who will visit Israel on Wednesday, said during a joint press conference with Palestinian Foreign Minister Riyad al-Maliki, "I am particularly concerned about the Israeli government's announcement of a major military operation in Rafah."

She added, "Of course, it is absolutely clear that in Rafah as well, there is an incredibly large network of the terrorist Hamas organization," adding that Israel has the right to defend itself from terrorism."

In London, British Foreign Secretary David Cameron described the October 7 attack on Israel that ignited the Gaza war as "the largest massacre since the Holocaust in terms of Jewish lives lost." He stressed that Israel "must obey international humanitarian law," meaning they must ensure humanitarian aid, water, food, and shelter are available to people in Gaza.

He explained that European, Arab, and U.S. officials plan to meet at the Munich Security Conference on Friday to discuss the situation, as well as efforts to push a two-state solution.

President Isaac Herzog is expected to attend the conference as well as King Abdullah.

At a joint press conference in Washington with Abdullah on Monday, Biden said, "The key elements of the deal are on the table, there are gaps remaining, but I encouraged Israeli leaders to continue working to achieve the deal."

He said, "The United States will do everything it can to make that happen."