"The inquiry into the event by the IDF is ongoing at this time. Initial findings show that terror activists were in the area that was attacked and that it served as a launching point for terror activities."
The IDF statement said that "it is a tragic event if innocent civilians were hurt in the incident." The military stressed that "it is important to remember the cynical use of Gaza Strip residents by Hamas who hold them as hostages has brought about the cancellation of attacks on terror targets, as has been proven in the past few days."
The statement noted that "the IDF has no intention to harm civilians hurled into the reality of war because of Hamas."
The four Palestinian children were killed on Wednesday afternoon on a Gaza beach by a shell fired by an Israeli naval gunboat, Palestinian medical officials said.
"The kids were playing football on the beach. They were all ... under the age of 15," said Ahmed Abu Hassera, 22.
"When the first shell hit the land, they ran away but another shell hit them all," said Abu Hassera, whose shirt was stained with blood.
"It looked as if the shells were chasing them," he told Reuters.
Ashraf al-Qidra, spokesman for the Gaza Health Ministry, said four of the youngsters were killed and a fifth youth was in critical condition. "This is a cowardly crime," he said.
The Gaza beach area has been shelled frequently since Israel began its offensive in the enclave on July 8 following a surge in Palestinian cross-border rocket strikes.
The IDF has been striking targets in Gaza City, Beit Lahia, Khan Younis on Wednesday since the early morning hours.
Reuters contributed to this report.