An Israeli four-hour cease-fire for parts of Gaza ended Wednesday, during which Gaza militants fired 27 rockets at Israel, and Palestinians claimed a strike hit a crowded market.
Hamas dismissed the "humanitarian" window and Israel said it would not halt fire in areas where the military is searching for tunnels used by Hamas militants.
Hamas spokesman Sami Abu Zuhri said it lacked any "value" because it excluded border areas from where Hamas wanted to evacuate the wounded.
Palestinian authorities claimed that an Israeli airstrike hit a crowded Gaza shopping area during the window, killing at least 16 people and wounding 150. The strike occurred in Shijaiyah, an area that was not included in the cease-fire.
Gaza health ministry official Ashraf al-Kidra and witnesses said the shopping area was busy because residents thought a cease-fire was in place. The Palestinian Red Crescent confirmed the death toll.
The Israeli military had no immediate comment and said it was investigating the report.
Earlier Wednesday Palestinian authorities said that a United Nations school was hit by Israeli tank shells, resulting in 15 deaths, and about 90 injuries, while the Israeli military said it fired after its soldiers were targeted by mortars operating from the vicinity of the school.
"In response, soldiers fired toward the origins of fire. And we're still reviewing the incident," the military said in a statement.
The United States condemned the shelling of the U.N. school, but did not say who was responsible.
White House spokeswoman Bernadette Meehan said the U.S. is also "extremely concerned" that thousands of Palestinians aren't safe in the U.N.-designated shelters in Gaza. The agency is sheltering more than 200,000 people displaced by the fighting at dozens of U.N. schools in Gaza.
Meehan said the U.S. also condemns those responsible for hiding weapons in U.N. facilities in Gaza, and the escalation shows the need for a cease-fire as soon as possible.
Abu Hasna, the U.N. agency spokesman called for the international community to step in.
"It's the responsibility of the world to tell us what we shall do with more than 200,000 people who are inside our schools, thinking that the U.N. flag will protect them," he said. "This incident today proves that no place is safe in Gaza."
Tank shells hit the U.N. school in Jebaliya refugee camp early Wednesday, Hasna said.
Starting at around 4:30 a.m., several shells hit the compound of the Abu Hussein school, a few minutes apart, said the principal, Fayez Abu Dayeh. He said shells hit two classrooms and a bathroom.
Assad Sabah said he and his five children were huddling under desks in one of the classrooms because of the constant sound of tank fire throughout the night.
"We were scared to death," he said. "After 4:30 a.m., tanks started firing more. Three explosions shook the school."
In one of the classrooms, the front wall was blown out, leaving debris and bloodied clothing. Another strike tore a large round hole into the ceiling of a second floor class-room.
Four of the dead were killed just outside the school compound, two in their home and two who were struck in the street after returning from pre-dawn prayers, their relatives said.
The shelling came amid the heaviest air and artillery assault by Israel against targets in Gaza since the beginning of Operation Protective Edge earlier this month.
The IDF claimed Wednesday it hit 75 sites, including five mosques it said were being used by militants to hide weapons and gain access to tunnels that extend into Israel. Hamas militants have used the tunnels to slip across the border between Israel and Gaza and attack Israeli soldiers and civilians. The IDF also claimed that it had destroyed three such tunnels in the previous 24 hours. In total, the Israeli army says that 32 tunnels have been located. However, it is not clear how many remain.
Health officials in Gaza say that at least 1,284 people have been killed in the violence, with more than 7,100 wounded. It is not clear how many of the Palestinian dead are civilians and how many are militants. Israel has lost 53 soldiers and three civilians.
Israel has vowed to stop the Hamas rocket and mortar fire that has reached increasingly deeper into its territory and to destroy a sophisticated network of Hamas military tunnels used for attacks in Israel.
The military said that since fighting began July 8, Israeli forces have hit 4,100 targets in Gaza, about one-third connected to the militants' ability to launch rockets at Israel. Over the same period, the IDF says, Hamas has fired over 2,670 rockets at Israeli civilians.
Israel says Hamas militants often launch rockets from crowded residential areas, thus endangering nearby civilians. The army says it has also given civilians a chance to leave dangerous areas by sending warnings in phone calls and leaflets.
On Wednesday, aircraft dropped leaflets over Gaza City's Rimal neighborhood. "The Israeli Defense Forces are going into a new phase in the coming operation and does not want to harm civilians," the leaflet said. "The army is warning residents in the areas where the operation will take place that for your safety, you have to keep away from terrorists and the locations from which they operate."
Hamas has so far rejected cease-fire efforts unless its demands are met, including a lifting of a punishing blockade.
The Associated Press contributed to this report.