“Impeding relief supplies as provided by the Geneva conventions may constitute a crime within the court jurisdiction,” Khan told reporters in Cairo on Sunday.
He added he wanted “to underline clearly to Israel that there must be discernible efforts without further delay to make sure civilians” in the Hamas-run Palestinian territory “receive basic food, medicines”.
“I saw trucks full of goods full of humanitarian assistance stuck where nobody needs them, stuck in Egypt, stuck at Rafah,” Khan continued.
“These supplies must get to the civilians of Gaza without delay.”
On Sunday, the United Nations warned it feared a breakdown of public order after looting at food aid centres in Gaza run by its agency for Palestinian refugees, UNRWA.
UN chief Antonio Guterres said the situation was “growing more desperate by the hour” as casualties in the war increase and essential supplies of food, water, medicine and shelter dwindle.
People in the Palestinian territory have lived under Israeli blockade for 17 years and under complete siege for the past three weeks.
The health ministry in Gaza announced that Israeli bombardment has killed more than 8,000 people, mainly civilians and half of them children.
Khan stated his office had an ongoing investigation into “any crimes committed on the territory of Palestine and any crimes committed, whether it’s by Israel and Palestine or whether it’s acts committed on the territory of Palestine or from Palestine into Israel”.
“This includes current events in Gaza and also current events in the West Bank,” Khan said, adding that he was “very concerned also by the spike of the number of reported incidents of attack by settlers against Palestinian civilians” in the territory Israel has occupied since 1967.
Khan also noted hostage taking was a breach of the Geneva Conventions.
“I call for the immediate release of all hostages taken from Israel and for their safe return to their families,” Khan said.
The British lawyer added “Israel has clear obligations in relation to its war with Hamas, not just moral obligations but legal obligations” to comply with the laws of conflict.
“These principles equally apply to Hamas in relation to firing indiscriminate rockets into Israel,” he continued.