Hamas has backed off some key demands in the negotiations for a hostage deal and pause in the fighting in Gaza following Israeli accusations that its position was “delusional,” bringing the negotiating parties closer to an initial agreement that could halt the fighting and see a group of Israeli hostages released, two sources familiar with the discussions say.

“The major obstacles have been resolved in terms of Hamas insisting on a full withdrawal of Israeli forces and end to the war,” a senior Biden administration official told CNN, following the Friday meeting in Paris between the US, Egyptian, Israeli intelligence chiefs and the Qatari prime minister.

“Hamas’ requirements for the numbers of Palestinians [prisoners that] would have to be freed has declined,” the official added.

A diplomatic source familiar with the discussions confirmed that Hamas softened its position ahead of an agreement on the first phase of a deal. Though it is expected that more challenging hurdles will emerge later when complex issues like Hamas releasing male IDF hostages and an end to the war will be discussed.

Those involved in the discussions have said an agreement would likely be implemented in multiple phases and once an initial deal is made it could lead to a truce lasting for a long as six weeks with a group of Israeli hostages released including women, children, the elderly and sick in exchange for a smaller number of Palestinian prisoners than Hamas had initially demanded.

The second phase is where discussions are expected to get even more complicated.

During a truce negotiations would take place over more sensitive topics like the release of Israeli soldiers who are hostages, Palestinian prisoners serving longer sentences, the withdrawal of IDF forces and bringing a permanent end to the war alongside the so-called “day after” issues.

Israeli leaders have made clear they intend to launch a military offensive into Rafah while in an earlier proposal Hamas said they want to use a second phase to discuss “the requirements necessary for the continuation of the mutual cessation of military operations.”

Teams from the countries that met on Friday in Paris were meeting Monday in Doha to discuss the finer points of the broad issues discussed Friday, a sign of progress.

“We did make progress in these conversations over the weekend and the last few days” to try to reach a deal to free the hostages and secure a temporary ceasefire, State Department spokesperson Matt Miller said Monday.

“We continue to believe that a deal is possible and we’re going to continue to pursue it,” Miller said at a department briefing.

Miller added that if Hamas “truly cared about the Palestinian people, they should agree to the deal that is on the table because it will greatly alleviate the suffering of those Palestinian people.”

On Sunday, US national security adviser Jake Sullivan declined to detail the terms were being discussed but said Friday’s meeting in Paris resulted in “an understanding among the four of them about what the basic contours of a hostage deal for temporary ceasefire would look like.”

“There will have to be indirect discussions by Qatar and Egypt with Hamas because ultimately they will have to agree to release the hostages,” Sullivan told CNN. “That work is underway. And we hope that in the coming days, we can drive to a point where there is actually a firm and final agreement on this issue. But we will have to wait and see.”

Israel confirmed on Monday that they were sending a team to Doha after Israeli Prime Minister Benjamin Netanyahu on Sunday was less dismissive of where the talks stand than he has been in the past few weeks.

“They have to come down to reality,” Netanyahu said of Hamas on Fox News. “And I think if that’s the case, we’ll be able to have a deal we certainly wanted, and I wanted.

Netanyahu is facing immense pressure from the Israeli public to free the more than 130 hostages who remain in Gaza, which includes the bodies of many who are believed to no longer be alive.

The embattled prime minister also reiterated that he plans to order the Israeli army into Rafah, which the US has warned it opposes without a firm plan that takes into consideration the safety of the around 1.5 million Palestinians concentrated there, many having fled the fighting farther north.

With or without a hostage deal, “We will do it anyway” Netanyahu told CBS News, because “total victory is our goal.”

“We can’t leave the last Hamas stronghold without taking care of it,” Netanyahu said.

This story has been updated with additional details.