The global agency's humanitarian office spokesperson Jens Laerke told journalists Israel had shut both the Rafah and Kerem Shalom crossings for aid and people as part of its military operation in Rafah, where around 1 million uprooted people are sheltering.
The Israeli military said a limited operation in Rafah was meant to kill fighters and dismantle infrastructure used by Hamas, which governs the besieged Palestinian territory.
"The two main arteries for getting aid into Gaza are currently choked off," Laerke said, adding U.N. agencies had very low stocks inside the Gaza Strip since humanitarian supplies were consumed immediately. The enclave has just a one-day buffer of fuel stocks, he said.
"If no fuel comes in for a prolonged period of time it would be a very effective way of putting the humanitarian operation in its grave," he said.
A World Health Organization spokesperson said in response to a journalist's question that no exceptions were being made for sick and injured patients.
While some non-fuel supplies have entered Gaza via the northern Erez crossing in recent days, the U.N. agencies said this was insufficient and difficult to deliver to Rafah since it meant crossing active combat zones.
"Erez will simply not be enough," said James Elder, a spokesperson for the United Nations children's agency. "If Rafah gate closes for an extended period, it's hard to see how famine in Gaza can be averted," he said.
Even before the latest escalation in the seven-month-old conflict, the United Nations has repeatedly accused Israel of restricting aid access despite famine warnings. Faced with growing international pressure, Israel had pledged to improve access but says U.N. agencies are to blame for not distributing aid more efficiently within the enclave.
U.N. agencies said they had pre-stocked some aid within Rafah but said there were very low supplies of water and high-energy nutrition supplies needed to treat malnourished children.