A White House official said on Sunday that reaching an agreement to secure the release of some hostages held in the Gaza Strip by activists of the Islamic Resistance Movement (Hamas) is closer than ever in the movement's war with Israel.

John Feiner, Deputy National Security Advisor at the White House, confirmed that the agreement to release "more than 12" hostages is likely to include an extended ceasefire and allow the distribution of humanitarian aid in Gaza.

Fighting broke out on Sunday, as Hamas militants fought Israeli forces attempting to infiltrate the largest refugee camp in Gaza, after Israeli and American officials denied a Washington Post report of an agreement.

Feiner told the "Meet the Press" program on NBC, "What I can say at this stage is that some of the outstanding areas of disagreement, in very complex and very sensitive negotiations, have been narrowed."

He added: "I think we are closer than we have been in a long time, and perhaps closer than we were since the beginning of this operation, to achieving this agreement."

Israeli Ambassador to the United States Michael Herzog also said in an interview with the ABC network's "This Week" program that Israel hopes Hamas can release a large number of hostages "in the coming days."

But Feiner warned, "Nothing will be agreed upon until everything is agreed upon. Sensitive negotiations like these can collapse at the last moment."

Hamas detained about 240 hostages during its deadly cross-border attack on Israeli communities on October 7, prompting Israel to impose a siege on Gaza and invade the Palestinian lands to eliminate the ruling Islamic group.

Feiner told NBC, "We are talking about much more than 12 (hostages)."

He added, "It is likely to include a long period of ceasefire for several days." He added, "We believe this will allow us to bring more humanitarian aid into Gaza. This is a priority under any circumstances."

Feiner also said that Israel should not conduct combat operations against Hamas in southern Gaza until military planners take into account the safety of fleeing Palestinian civilians.

Feiner said on the CBS "Face the Nation" program in a separate interview, "If Israel is likely to embark on combat operations including in the south, we believe... it has the right to do so."

He added, "We believe their operations should not proceed until these people, these additional civilians, are considered in their military planning."

The swift Israeli attack has turned large areas of the north into rubble, while about two-thirds of Gaza’s 2.3 million residents have been displaced to the south.

The Gaza Health Ministry raised the death toll from Israeli bombings to 12,300, including 5,000 children.

Feiner urged Israel to learn lessons from its military operations in northern Gaza and provide enhanced protection for civilians by narrowing the combat zone and identifying places where civilians can take refuge.

Israel warned civilians on Saturday in parts of southern Gaza to move to other areas as it prepares for a northern attack.

Palestinians say the south has been frequently bombed by Israel, making Israeli promises of security laughable.

In the same context, Qatari Prime Minister Mohammed Al Thani said today (Sunday) that efforts to free hostages held in the Gaza Strip continue, and that he is now more confident of reaching an agreement for their release.

Al Thani confirmed during a press conference held in Doha in the presence of EU Foreign Minister Josep Borrell that "the differences between the two parties regarding the hostage issue are very minimal, and the points of disagreement are logistical."