The Israeli military has called on residents to evacuate several neighborhoods in Gaza City, the latest in a series of orders that have forced Palestinians to flee as Israel again escalates its offensive against Hamas in the war-battered Gaza Strip.

The new evacuation order late Thursday came not long after the Palestinian health authorities said dozens of people, including children, were killed in Israeli strikes on a school turned shelter in Gaza City. Israel said it was looking into the episode.

The departure order has brought renewed hardship to Palestinians who had already endured displacement from their homes and miserable conditions during the first 15 months of the war. A shaky two-month-old cease-fire between Israel and Hamas collapsed in mid-March after they failed to reach an agreement to extend it, ending a brief respite for Palestinians in Gaza.

The Israeli military has since embarked on a major bombing campaign throughout Gaza that Israeli officials have said was intended to compel Hamas to release more hostages. Avichay Adraee, the military’s Arabic-language spokesman, said in a post late Thursday on social media that he was providing a “final” warning before a new attack, urging people to relocate southward. Mr. Adraee suggested that militant groups were operating among civilians in the area.

While many people have complied with such evacuation orders from the military during the most recent Israeli campaign, others have chosen to stay in their homes or shelters, saying they could not bear being displaced — many of them have already been uprooted several times during the war — or that they have nowhere else to go.

The Israeli military has said it was looking into reports about the Thursday incident in the Tuffah neighborhood of Gaza City. As of Friday morning, it said it still could not comment.

On Wednesday, Mr. Adraee had called for people to leave Tuffah. His order on Thursday was for other parts of the city.

Multiple videos verified by The New York Times on Thursday show an explosion and its chaotic aftermath at the Dar al-Arqam school, where civilians were sheltering. The strikes were followed by a chaotic scene at Al Ahli Arab Hospital in Gaza City, where dust-covered and bloodied children were rushed from vehicles.

The bodies of 27 people killed in the strike arrived at the hospital, the Gaza health ministry said. The ministry does not distinguish between civilians and combatants in its casualty counts.

One of those killed was the grandson of Khalil al-Hayya, Hamas’s top negotiator based in Qatar, the Hamas-run Al Aqsa TV channel reported.

Israel has previously targeted schools being used as shelters, contending that Hamas militants were operating command centers in them. Hamas has denied such claims in the past. The United Nations has said that Israeli strikes on schools probably violated the law by causing disproportionate harm to noncombatants.

More than 1,000 people in Gaza have been killed since the collapse of the cease-fire on Mar. 18 and more than 50,000 people have been killed since the start of the war, according to the Gaza health ministry. The war started after Hamas-led forces attacked Israel, killing roughly 1,200 people.

Nader Ibrahim contributed reporting.