Nearly three dozen trucks entered Gaza on Sunday in the largest aid convoy since the war between Israel and Hamas began, even as Israeli forces ramp up what is now being called a “second stage” in the war against Hamas terrorists in the region.

Communications were restored to most of Gaza’s 2.3 million people Sunday after an Israeli bombardment described by residents as the most intense of the war knocked out phone and internet services late Friday.

On Sunday, 33 trucks carrying water, food and medicine entered the only border crossing from Egypt, a spokesperson at the Rafah crossing, Wael Abo Omar, told The Associated Press.

After visiting the Rafah crossing, the chief prosecutor of the International Criminal Court, Karim Khan, called the suffering of civilians in the strip “profound” and the Hamas attack that precipitated the war a serious violation of international law.

“The burden rests with those who aim the gun, missile or rocket in question,” he said, putting responsibility for the conflict clearly on the shoulders of Hamas’ leaders.

The Israeli military said Sunday it had struck more than 450 militant targets over the past 24 hours, including Hamas command centers and anti-tank missile launching positions. Huge plumes of smoke rose over Gaza City. A spokesman for the Israeli military, Rear Admiral Daniel Hagari, said dozens of militants were killed.

Mr. Hagari also blamed Hamas’ leader in Gaza, Yehya Sinwar, for bringing destruction upon his people. “We will chase him until we get him,” he said.

The Hamas military wing said its militants clashed with Israeli troops who entered the northwest Gaza Strip with small arms and anti-tank missiles. Palestinian militants have continued firing rockets into Israel.

President Joe Biden in a call with Netanyahu on Sunday “underscored the need to immediately and significantly increase the flow of humanitarian assistance to meet the needs of civilians in Gaza,” a White House statement said. Israeli authorities said they would soon allow more humanitarian aid to enter Gaza.

But the head of civil affairs of COGAT, the Israeli defense body responsible for Palestinian civilian affairs, provided no details on how much aid would be available. Elad Goren also said Israel has opened two water lines in southern Gaza within the past week. The AP could not independently verify that either line was functioning.

Israel says most Gaza residents have heeded its orders to flee to the southern part of the besieged territory, but hundreds of thousands remain in the north, in part because Hamas terrorists have blocked them from escaping in order to use them as human shields.

The military escalation has increased domestic pressure on Israel’s government to secure the release of some 230 hostages seized by Hamas during the October 7 attack. Hamas says it is ready to release all hostages if Israel releases all of the thousands of Palestinians held in its prisons, but has dismissed the Hamas offer.

“If Hamas does not feel military pressure, nothing will move forward,” Israeli Defense Minister Yoav Gallant told families of the hostages Sunday.

The Israeli military has stopped short of calling its gradually expanding ground operations inside Gaza an all-out invasion. Casualties on both sides are expected to rise sharply as Israeli forces and Palestinian militants battle in dense residential areas.

Israel says it targets Hamas fighters and infrastructure and that the militants operate among civilians, putting them in danger. More than 1.4 million people across Gaza have fled their homes.

The fighting has raised concerns that the violence could spread across the region. Israel and the Lebanese terrorist group Hezbollah have engaged in daily skirmishes along Israel’s northern border.

Mr. Hagari said Israel on Sunday struck three militant cells that fired from Lebanon into Israel and killed militants who were trying to enter. Hamas said its forces in Lebanon fired 16 missiles at the Israeli city of Nahariya. Hezbollah, a Hamas ally, said it also fired missiles at several sites.

The Israeli military said Sunday night that rockets from Syria fell in open Israeli territory. It did not report any injuries.