The United Nations human rights office said on Tuesday that the wilful impediment of access to food and relief for civilians in Gaza may constitute a war crime, describing attacks on civilians trying to access food aid as unconscionable.

"For a third day running, people were killed around an aid distribution site run by the 'Gaza Humanitarian Foundation'," the spokesperson for the U.N. High Commissioner for Human Rights Jeremy Laurence told reporters in Geneva.

At least 27 Palestinians were killed and dozens wounded by Israeli fire near a food distribution site in the southern Gaza Strip on Tuesday, local health authorities said, in the third day of chaos and bloodshed to affect the aid operation.

The Israeli military said its forces had opened fire on a group of individuals who had left designated access routes near the distribution center in Rafah. On June 1, some 32 people were killed and on Monday three people were killed, according to the OHCHR.

The head of the U.N. agency, Volker Turk, urged a prompt and impartial investigation into attacks on Palestinians trying to receive food aid.

"Attacks directed against civilians constitute a grave breach of international law, and a war crime," Turk said in a statement.

The U.S.-backed Gaza Humanitarian Foundation launched its first distribution sites last week in an effort to alleviate widespread hunger amongst Gaza's war-battered population, most of whom have had to abandon their homes to flee fighting.

The foundation's aid plan, which bypasses traditional aid groups, has come under fierce criticism from the United Nations and established charities which say it does not follow humanitarian principles.

The private group, which is endorsed by Israel, said it distributed 21 truckloads of food early on Tuesday and that the aid operation was "conducted safely and without incident within the site."