The Israeli military issued new evacuation orders in the Gaza Strip on Thursday, forcing more Palestinians to flee their homes and shelters, as the United States and others tried to salvage sputtering talks that could ease regional tensions and stop the 10-month war.

Thousands of civilians were already on the move, responding to Israeli orders issued a day earlier to leave several neighborhoods in central Gaza. Most of them have been displaced multiple times over the course of the war.

Mohammed Aborjela was among those who fled the city of Deir al-Balah, in central Gaza, after he received a phone message from the Israeli military on Wednesday afternoon warning that it would act “forcefully” against Hamas militants in the area.

Mr. Aborjela, 28, packed up the few belongings he had and headed to Al-Mawasi, a coastal area that Israel has declared a humanitarian zone, but that has come under attack numerous times. Hours after he arrived there, he said, shelling from tanks reached tents where people were sheltering.

“The tanks got close to us,” Mr. Aborjela said. “And they started shelling the people even though it is supposed to be a safe zone.”

The Israeli military, asked whether its tanks had fired toward Al-Mawasi, said it “takes feasible precautions to mitigate civilian harm.” It said that Israeli forces had “intensified” operations in the Deir al-Balah area after intelligence indicated the presence of Hamas infrastructure and fighters on the outskirts there and in the southern city of Khan Younis.