There are "very serious discussions and negotiations" for a second truce between Israel and Hamas that would secure the release of dozens of hostages, according to a United States official.

Ismail Haniyeh, the top political leader of Hamas, traveled to Cairo on Wednesday to meet with Egyptian officials about a proposal, while Israeli leaders have also signaled a willingness to return to the negotiating table about three weeks after the first and only ceasefire in the war collapsed.

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The framework of a deal, which could still change, would include the release of roughly 40 hostages — women, elderly men, and anyone in need of urgent medical care — in exchange for a weeklong ceasefire and the possibility of more Palestinian prisoners being released, according to Axios.

"Israel is ready for another humanitarian pause and additional humanitarian aid in order to enable the release of hostages," Israeli President Isaac Herzog told a gathering of ambassadors from more than 80 nations on Tuesday. The presidential position in Israel's government is largely ceremonial, while the prime minister position is the head of the executive branch.

The first pause in fighting allowed for about 120 hostages to be freed, while there are about 130 held captive by Hamas since the Oct. 7 terrorist attacks who still remain in Gaza.

Herzog went further during an Atlantic Council event, also on Monday, when he declared, "Israel is willing to enter another humanitarian pause and bring in additional humanitarian aid in order to bring back the hostages," and he put the fate of a possible ceasefire directly on Hamas's leader, Yahya Sinwar. "The entire responsibility for this issue lies with Sinwar and with his people."

The first ceasefire agreement that Israel and Hamas reached, through U.S., Qatari, and Egyptian intermediaries, called for Hamas captors to release the women and children they held in exchange for three times as many Palestinians held in Israeli prisons, which took place on a daily basis. The deal fell apart when Hamas failed to provide a list of hostages who would be released and fired rockets in violation of the agreement, which ultimately led Israel to restart its war efforts.

"There’s no expectation at this point, but we are pushing” for a deal, President Joe Biden told reporters on Wednesday, while National Security Council coordinator John Kirby said, "These are very serious discussions and negotiations, and we hope they’ll lead somewhere."

Former Israeli Ambassador to the U.S. Michael Oren told the Washington Examiner that he anticipates another deal will be agreed upon, though he warned that stopping the military campaign could give Hamas time to plan additional attacks targeting Israeli forces. He also speculated that the new agreement could include the release of Palestinians accused of or found guilty of more serious crimes than those of the group of Palestinians released during the initial ceasefire.

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"The noose is tightening around Yahya Sinwar's neck and the more pressure Israel brings to bear on Hamas, which is pretty much confined to underground, the more willing they will be to negotiate for hostages' release," Oren said. "Keep in mind that Hamas's goal is to transform a temporary ceasefire into a permanent ceasefire and to establish ceasefires as the norm."

There are still eight Americans believed to be held in Gaza.