By David Morgan and Jasper Ward
WASHINGTON (Reuters) -A deal to secure the release of some of the hostages held in Gaza by Hamas militants is closer than ever in the Islamist group's war with Israel, a White House official said on Sunday.
White House deputy national security adviser Jon Finer said an agreement to free "considerably more than 12" hostages would also likely include an extended pause in the fighting and allow for the distribution of humanitarian assistance in Gaza.
Fighting raged on Sunday, with Hamas militants battling Israeli forces trying to push into Gaza's largest refugee camp, the day after Israeli and U.S. officials denied a Washington Post report that a deal had been reached.
"What I can say at this point is that some of the outstanding areas of disagreement, in a very complicated, very sensitive negotiation, have been narrowed," Finer told NBC's "Meet the Press" program.
"I believe we are closer than we have been in quite some time, maybe closer than we have been since the beginning of this process, to getting this deal done," he added.
Israeli Ambassador to the United States Michael Herzog also said in an interview on ABC's "This Week" that Israel is hopeful a significant number of hostages could be released by Hamas "in coming days."
But Finer cautioned: "Nothing is agreed until everything is agreed. Sensitive negotiations like this can fall apart at the last minute."
Hamas took about 240 hostages during its deadly cross-border rampage into Israeli communities on Oct. 7, which prompted Israel to lay siege to Gaza and invade the Palestinian territory to eradicate its ruling Islamist group.
"We're talking about considerably more than 12 (hostages)," Finer told NBC.
"This could and would likely include an extended period of a pause in the fighting, a multiple-day period," he added. "It would enable us, we believe, to get more humanitarian assistance into Gaza. That's a priority under any circumstances."
Finer also said Israel should not conduct combat operations against Hamas in the south of Gaza until military planners have taken into account the safety of fleeing Palestinian civilians.
"In the event that Israel is likely to embark on combat operations, including in the south, we believe ... that they have the right to do that," Finer told CBS' Face the Nation program in a separate interview.
"We think that their operations should not go forward until those people, those additional civilians, have been accounted for in their military planning," he said.
Israel's blitz has reduced swaths of the north to rubble, while some two-thirds of Gaza's population of 2.3 million have been displaced to the south.
Gaza's Health Ministry has raised its death toll from Israeli bombardment to 12,300, including 5,000 children.
Finer urged Israel to draw lessons from its military operations in the north of Gaza and provide enhanced protections for civilians by narrowing the area of active combat and by specifying where civilians can seek refuge.
On Saturday, Israel warned civilians in parts of southern Gaza to relocate as it girds for an offensive from the north.
The south has been repeatedly bombarded by Israel, rendering Israeli promises of safety absurd, Palestinians say.
(Reporting by David Morgan and Jasper Ward, additional reporting by Leah Douglas; Editing by Scott Malone and Bill Berkrot)