The head of the U.N. Palestinian refugee agency said on Thursday that crowds of hungry people were stopping its aid trucks in Gaza and helping themselves to the food, making it almost impossible to continue delivering aid.

The U.N. World Food Programme has said half of Gaza's population of 2.3 million is starving as Israel's military assault on the southern part of the enclave expands and people are cut off from supplies.

"People are stopping aid in trucks, taking the food and eating it right away. And this is how desperate and hungry they are," Philippe Lazzarini, UNRWA commissioner-general, told reporters at the Global Refugee Forum in Geneva.

Huge crowds on the street also mean that it is harder to reach hundreds of thousands of people in U.N. shelters in southern Gaza, Lazzarini said, speaking after a trip to Gaza.

"Hunger has now emerged over the last few weeks and we meet more and more people who haven't eaten for one two or three days," he added.

"...Our operating environment becomes more and more difficult. And the only way at this stage, in the absence of a ceasefire, to address it and to reverse this tension is to bring assistance at scale," Lazzarini said.

Aid deliveries crossing into Gaza via the sole entry point on the Egyptian border are only a fraction of pre-conflict levels despite the surge in needs.

Israel says it has ramped up aid inspection capacity and reopened the Kerem Shalom crossing for checks this week to ease flows.

According to U.N. estimates, up to 85% of the 2.3 million people in Gaza - one of the most densely populated areas of the world - have been displaced from their homes and are now crammed in an ever smaller area in the south near the border with Egypt.

Lazzarini said aid deliveries were focused on southern and middle areas of Gaza but that it has become "excruciatingly difficult" to get aid to people remaining in northern Gaza since a seven-day pause in the conflict ended on Dec. 1.