GENEVA (Reuters) - The U.N. aid chief warned on Thursday that famine was an immediate risk in Gaza with food stocks running out, describing fresh challenges since the start of the Israel's Rafah operation that made planning and distributing relief almost impossible.

As Israel has pounded southern Gaza, some 600,000 people or about half of the uprooted population sheltering there have fled to other areas of the besieged enclave, sometimes returning to bombed out houses or empty fields.

Martin Griffiths said the global body was struggling to help them, with imports of aid all but blocked through southern Gaza and fresh fighting adding to distribution challenges.

"Stocks of food which were in place already in southern Gaza are running out. I think we're talking about almost none left," Martin Griffiths told Reuters in an interview in Geneva.

"And so the humanitarian operation is stuck, it's completely stuck. We can't do what we want to do," he said, calling the relief operation "unplannable".

Israel's military says its operation in Rafah is meant to kill Hamas fighters and dismantle infrastructure used by the group, which governs the blockaded Palestinian territory. Israel accuses Hamas of diverting aid, something it denies.

(Reporting by Emma Farge; Editing by Alex Richardson, William Maclean)

By Emma Farge