(JNS) Negotiators have made “real progress” over the last few weeks on the framework for an agreement to free the remaining Israeli hostages held by Hamas in Gaza, a senior Biden administration official said on Sunday.

However, the official told Reuters, there are still “significant” gaps to close, adding that “it’s pretty much there.”

The potential hostage release deal was the main focus of a 45-minute phone call between Israeli Prime Minister Benjamin Netanyahu and US President Joe Biden on Sunday.

Biden stressed “the need to capitalize on progress made in the negotiations to secure the release of all hostages as soon as possible,” according to a White House readout of the call.

It was the first time the two men have spoken since Biden described Jerusalem’s response to Hamas’s October 7 massacre as “over the top” late last week.

The president also “reaffirmed our shared goal to see Hamas defeated and to ensure the long-term security of Israel and its people,” according to the White House.

An Israeli political source characterized the conversation as “good” and said discussions focused on the looming ground operation in the Hamas stronghold of Rafah, the issue of aid to Gaza and the hostage release negotiations.

Egypt has warned Hamas that it must agree to a hostages-for-ceasefire deal with Jerusalem within two weeks to avert an Israel Defense Forces operation in the terrorist group’s last bastion in the Gaza Strip, the southernmost city of Rafah, The Wall Street Journal reported on Sunday.

This week, Israel will reportedly dispatch to Cairo negotiators to discuss a new hostage deal with US, Egyptian and Qatari officials.

Mossad chief David Barnea, Israel Security Agency (Shin Bet) head Ronen Bar and Maj. Gen. Nitzan Alon, who is overseeing the IDF’s efforts to find the hostages, will meet with CIA director Willian J. Burns, Qatari Prime Minister Mohammed bin Abdulrahman Al Thani and Maj. Gen. Abbas Kamel, the head of Egypt’s General Intelligence Directorate.

On Sunday, Israeli Defense Minister Yoav Gallant said intelligence recovered by the IDF in Gaza is making a “realistic” deal possible.

“We penetrated into the heart of Hamas’s most sensitive places and are using their intelligence against them,” said Gallant. “The more we deepen this operation, the closer we are to a realistic deal in order to return the captives.”

Netanyahu has insisted that consistent military pressure against the terrorist group in Gaza is the most effective way to secure the release of the hostages. Israeli forces in Gaza freed two hostages in an overnight mission Monday in Rafah.

It was the second successful hostage rescue operation undertaken by the IDF in Gaza. So far, 112 captives have been freed, including 105 in a hostage deal in late November. A total of 134 remain in Hamas captivity, with 32 confirmed dead and another 20 feared no longer alive.

Hamas warned on Sunday that any Israeli ground offensive in Rafah would “blow up” the hostage release negotiations.

Separately, opposition leader and former Prime Minister Yair Lapid met with French President Emmanuel Macron in Paris to discuss international efforts to bring the hostages home and to remove the threat of the Iranian terrorist proxy Hezbollah at the border with Lebanon.