KYIV, Ukraine >> The head of the U.N. World Food Program said people are being “starved to death” in the besieged Ukrainian city of Mariupol, and he predicted the country’s humanitarian crisis is likely to worsen as Russia intensifies its assault in the coming weeks.

WFP executive director David Beasley also warned in an interview Thursday with The Associated Press in Kyiv that Russia’s invasion of grain-exporting Ukraine risks destabilizing nations far from its shores and could trigger waves of migrants seeking better lives elsewhere.

The war that began Feb. 24 was “devastating the people in Ukraine,” he said, lamenting the lack of access faced by the WFP and other aid organizations in trying to reach those in need amid the conflict.

“I don’t see any of that easing up. I just don’t see it happening right now,” he said.

The fluid nature of the conflict, which has seen fighting shift away from areas around the capital and toward eastern Ukraine, has made it especially difficult to reach hungry Ukrainians.

The WFP is trying to put food supplies now in areas that could be caught up in the fighting, but Beasley acknowledged that there are “a lot of complexities” as the situation rapidly evolves.

A lack of access is part of the problem, he said, but so is a shortage of manpower and fuel as resources are diverted to the war effort.

“It’s not just going to be the next few days — but the next few weeks and few months could even get more complicated than it is now,” he said. “In fact, it’s getting worse and worse, concentrated in certain areas, and the front lines are going to be moving.”

Beasley expressed particular concern about the port city of Mariupol, where a dwindling number of Ukrainian defenders is holding out against a Russian siege that has trapped well over 100,000 civilians in desperate need of food, water and heating.

Russian forces that control access to the city have not allowed in aid, even though the WFP has demanded access.

“We will not give up on the people of Mariupol and other people that we cannot reach. But it’s a devastating situation: the people being starved to death,” he said.

Russia is determined to seize the city so its forces from the annexed Crimean Peninsula can fully link up with troops elsewhere in the eastern Donbas region, Ukraine’s industrial heartland and the target of the coming offensive.

The U.N. food chief warned of disastrous ripple effects due to Ukraine’s role as major international grain supplier.

A global food shortage caused by the war could prompt “mass migration beyond anything we’ve seen since World War II,” he said, echoing remarks he made to the U.N. Security Council last month.

Russia and Ukraine together produce 30% of the world’s wheat supply and export about three-quarters of the world’s sunflower seed oil. Half of the grain the WFP buys for distribution around the world comes from Ukraine.

Some 30 million metric tons of grain bound for export are unable to be shipped because of the war, Beasley said. Ukrainian farmers are struggling to access fertilizer and seed, and those who can plant may see their harvest rot in the fields if the war drags on and there’s no way to ship it, he warned.

The shipping challenges have forced the WFP to halve rations for millions of people, many in Africa, and more cuts may be needed, he said.

“People are going to be starving to death,” he said.

Beasley also visited areas near Kyiv that were ravaged by the Russian invasion, including the town of Bucha, where evidence of mass killings and other atrocities against civilians have shocked the world.

He described neighborhoods “completely decimated by bombings,” likening what he saw to a nightmare that was impossible to believe.

But he stopped short of describing the killings a genocide, as U.S. President Joe Biden did this week.

“Well, I know one thing. People are dying,” he said when asked about Biden’s comments. “But there’s no doubt in my mind this is a horror story and it is truly heartbreaking.”