Israeli forces showed no signs of relenting on their new ground offensive in Gaza City on Monday as world leaders gathered in New York for the United Nations General Assembly, and more countries prepared to join the surge of nations recognizing a Palestinian state.

Hundreds of thousands have remained in the city, the territory's largest and already in ruins from nearly two years of war and struggling with famine. The Israeli military ordered the evacuation on Monday of the Jordanian Hospital, a key health clinic, a Palestinian health official said.

The latest Israeli operation, which started last Tuesday, further escalates a conflict that has roiled the Middle East and likely pushes any ceasefire further out of reach. The Israeli military, which says it wants to "destroy Hamas' military infrastructure," hasn't given a timeline for the offensive, but there were indications it could take months.

Many have been attempting to relocate from the city, where 1 million people once lived, to the southern Gaza Strip, following Israeli military calls for a full evacuation.

Site Management Cluster, whose figures are widely trusted by the U.N. and humanitarian groups, said its teams counted about 297,597 "movements" from Gaza City toward the south between Aug. 14 and Sept. 20.

The organization uses the term "movements" in case the same displaced person moves more than once. But in reality, field monitoring teams say nearly all movements are people fleeing the city.

They monitor the number of people moving during daytime hours through four locations in Gaza, meaning the figure could be an undercount.

Israel's military claims that over 500,000 Palestinians have left the city.

Hundreds of thousands of Palestinians are still sheltering in the city as troops move in.

Some Palestinians fleeing Gaza City said they see the flurry of recognitions as "a glimmer of hope" and urged other countries to join the move.

The Jordanian field hospital in the city's southwestern neighborhood of Tal al-Hawa received orders to evacuate on Monday morning, according to a senior health official.

The military has already ordered all Palestinians in Gaza City to head south, to central and southern Gaza Strip. It has told aid workers in private messages that all humanitarian sites — except hospitals — must evacuate.

The military didn't immediately respond to a request for comment.

Dr. Muneer al-Boush, director general of the Gaza Health Ministry, told The Associated Press that the hospital has at least 300 patients, as well as medical staff and family members of the patients.

The order came as residents reported that troops were approaching the facility, with dozens of families trapped in their homes and shelters around the hospital.