The comments came during a UN Security Council debate discussing an annual report by Ban's office on children and armed conflict, which drew criticism when it was released last week for not including Israel on the list that violate children's rights.
The report said that at least 557 Palestinian killed during the 50-day war in Gaza last year, while 4,249 Palestinian were injured.
Ban said during the Security Council briefing that he was "deeply alarmed" by the suffering of children as a result of Israeli military operations.
"I urge Israel to take concrete and immediate steps, including by reviewing existing policies and practices, to protect and prevent the killing and maiming of children, and to respect the special protections afforded to schools and hospitals," Ban said.
The document devoted 32 paragraphs to Israel and 17 paragraphs to Syria, where children suffer the effects of an ongoing civil war and the brutality of the so-called “Islamic State” extremist groups.
Riyad Mansour, Palestinian ambassador the UN, told the council that while there's enough evidence to include Israel on the list of violators, the Zionist was not included "as pressures were again blatantly exerted to shield it from censure and measures of accountability."
"This glaring omission and failure to hold Israel responsible for its crimes comes at a heavy cost to our innocent children," Mansour said.
He also circulated a nine-page document listing the names and ages of children killed during the Gaza conflict last year.
Defending his decision not to include Israel on the list of violators, Ban said he regretted that the annual report was "the subject of more controversy and discussions than usual" but said that the report has withstood scrutiny and its content "should speak for itself."
The war in Gaza killed more than 2,200 Palestinians.