The United States believes eight Americans are still being held hostage by militants in the war-torn Gaza Strip, according to White House National Security Council spokesperson John Kirby.

"We think there's about eight hostages that are Americans. We know of at least one woman in that group," Kirby told ABC News' George Stephanopoulos in an interview Wednesday on "Good Morning America."

"We're doing everything we can to try to get them released," he continued. "We're constantly engaged with our partners in the region to try to get this humanitarian pause back in place, so that the flow of hostages can renew."

Although a temporary cease-fire between Israel and Gaza's militant rulers, Hamas, ended last week, the U.S. is "still flowing in humanitarian assistance" to civilians in Gaza, according to Kirby.

"And we're trying to get it up to the level that it was during the pause," he noted.

When asked about what Israel's "endgame" might be in its war against Hamas as Israeli troops expand their offensive across all of Gaza, Kirby said: "That's really something for the Israeli's to speak to."

"We obviously want to see Hamas eliminated as a threat to the Israeli people," he added. "That hasn't been achieved yet. They're going after the leadership as best they can. They believe they need to operate in the south. We've told them you know we’ll continue to support their military operations but we want to make sure that as they do that they're factoring in those innocent civilian lives as much as possible."

-ABC News' Morgan Winsor

Al-Awda Hospital in the northern Gaza Strip is "besieged" by Israeli forces, a spokesperson said Wednesday.

There are currently 95 employees and 38 patients inside the hospital in the city of Jabalia, north of Gaza City, according to the spokesperson.

Just four hospitals remain operational in the north, according to the Gaza's Hamas-run Ministry of Health.

-ABC News' Nasser Atta and Morgan Winsor

A hospital in the Middle Area of the Gaza Strip has seen an influx of dead and wounded arrive at its doors over the last day, according to Palestinian health officials.

Gaza's Hamas-run Ministry of Health said Wednesday morning that the Al-Aqsa Martyrs Hospital has received 73 dead and 123 injured patients in the past 24 hours amid intense bombardment by the Israeli military.

-ABC News' Nasser Atta and Morgan Winsor

More than 1,000 Americans and their family members are still stranded in Gaza, more than a month after the Rafah border crossing first opened to outbound traffic, according to the State Department.

"We know of approximately 1,050 individuals (about 350 U.S. citizens, plus lawful permanent residents and family members of U.S. citizens and lawful permanent residents) who we are in touch with and who are seeking to depart Gaza," a State Department spokesperson said in a statement to ABC News, adding it "remains a fluid and quickly evolving situation."

These figures come a day after State Department spokesperson Matt Miller told reporters that the number of American citizens trying to exit the area stood at 220, and that there were 750 individuals eligible to leave Gaza who had not yet been able to depart.

-ABC News' Shannon K. Crawford

Over 600 foreign passport holders -- nearly half of whom are Americans and Canadians -- were on a list of people approved to leave Gaza on Sunday. Some 566 foreign passport holders, whose nationalities were not released, later exited the Gaza Strip through Egypt’s Rafah border crossing on Sunday, crossing spokesman Wael Abu Omar told ABC News.

Thirteen wounded Gaza residents and 11 of their family members also left Gaza and entered Egypt on Sunday, the spokesman said.

-ABC News' Ayat Al-Tawy