“It’s a perfect storm within a perfect storm,” said David Beasley, the executive director of the World Food Program, a United Nations agency. Calling the situation “absolutely critical,” he warned, “We will have famines around the world.”

The world’s food distribution network was already strained by pandemic-related disruptions, and exports from Ukraine, ordinarily among the world’s biggest suppliers, have plummeted because of the war. Russia has seized some the country’s Black Sea ports and blockaded the rest, trapping cargo vessels laden with corn, wheat, sunflower seeds, barley and oats.

Russian forces have taken control of some of Ukraine’s most productive farmland, destroyed Ukrainian infrastructure that is vital to raising and shipping grain, and littered farm fields with explosives. Ursula von der Leyen, the president of the European Union’s executive branch, told the political and business leaders gathered in Davos that Russia — an even bigger exporter — had confiscated Ukrainian grain stocks and agricultural machinery.

“On top of this,” she said, “Russia is now hoarding its own food exports as a form of blackmail, holding back supplies to increase global prices, or trading wheat in exchange for political support.”

The fighting in Ukraine is increasingly concentrated in a small pocket of the Donbas region of eastern Ukraine, where Russia’s battered forces are making slow, bloody progress as they try to encircle the strategically important city of Sievierodonetsk, the easternmost Ukrainian stronghold.

Within the city, once an industrial hub, the devastation from Russian artillery is evident on every street in the form of shattered buildings, burned-out vehicles and cratered pavement. Russian pincers approaching the city from the north and south are separated by just 16 miles, but face “strong Ukrainian resistance,” the British Defense Ministry said on Tuesday.

Three months into the war, the United States and its allies have shown remarkable solidarity so far in supporting Ukraine with weapons and other aid, and in punishing Russia with economic sanctions, but the limits of that unity are being tested. Finland and Sweden have signaled that they want to abandon their long-held neutrality to join NATO, but that plan is being held up by one member country, Turkey. At the same time, Hungary is blocking an E.U. plan to embargo imports of Russian oil.

Within both blocs, officials have offered assurances, without specifics, that the roadblocks will soon be overcome. Jens Stoltenberg, the NATO secretary general, said Tuesday that he was confident Sweden and Finland would join the alliance, though “I cannot tell you exactly how and when.” Diplomats from the two Nordic countries traveled to Turkey for talks on the issue.

The European Union, heavily dependent on Russian fuels, has already agreed to a phased embargo on natural gas from Russia, and the head of the International Energy Agency, Fatih Birol, warned that Europe could face gas rationing next winter.

“I’m advising several European governments to prepare a contingency plan,” Mr. Birol said at Davos. He added that “Europe is paying for its over-dependence on Russian energy.”

Ukraine has applied to join the European Union, and on Tuesday its government rejected a French proposal for something short of full membership. Russia has vehemently opposed any expansion of NATO and E.U. membership for Ukraine, but its aggression has backfired, making those associations more attractive to its neighbors.

Increasingly isolated, the Kremlin has looked to Beijing for support, and Russia held joint military maneuvers on Tuesday with China, their first since the war in Ukraine began. The show of force included bomber flights over the Sea of Japan, while President Biden was not far away, in Tokyo, for meetings with world leaders.

But the food crisis took center stage at Davos, where President Andrzej Duda of Poland warned that famine in Africa and elsewhere would prompt a flood of migration to Europe, where searing memories are fresh of the 2015-2016 migration wave that strained E.U. unity and empowered xenophobic nationalist movements.

Ukraine and Russia ordinarily account for about one-quarter of the grain traded internationally; in recent years, Ukraine had exported an average of about 3.5 million tons of per month. In March, only 300,000 tons were shipped out, though exports rebounded somewhat to more than a million tons in April and could reach 1.5 million tons in May, said Roman Slaston, the chief of Ukraine’s agricultural industry group.

Ukraine’s agriculture ministry says that the Black Sea blockade has prevented 14 million tons of corn, 7 million tons of wheat and 3 million tons of sunflower seeds from reaching world markets. Ukrainian officials have accused Moscow of stealing Ukraine’s produce and then selling it abroad as Russian.

Western officials are circulating proposals for getting grain out of Ukraine, such as having multiple countries send warships to escort cargo ships from Ukrainian ports and run the blockade, but that runs the danger of a shooting confrontation with Russian vessels. Sending ships from NATO countries is considered particularly risky — like the rejected idea of having NATO members enforce a no-fly zone to keep Russian warplanes away from Ukraine — so much of the talk has been about countries outside the alliance taking part.

But Mr. Stoltenberg, the NATO chief, warned that breaking the Black Sea blockade would be very hard.

“Is it possible to get it out on ships? That is a difficult task. It’s not an easy way forward,” he said.

Ukraine has continued to ship grain overland through Europe, and work is underway to expand such routes, Ms. von der Leyen and Mr. Slaston said — but doing so on a scale great enough to replace seagoing shipment would be very difficult. The railways in Eastern Europe use different gauges, which means switching equipment when going long distances, and many of Ukraine’s railroads, highways and bridges have been damaged by Russian attacks.

One farmer said he lost 50 rail cars full of grain when his cargo got stranded between Russian airstrikes in front of and behind the train.

But the problem is not limited to shipping — farming, itself, has been greatly diminished by the war. In some places, fighting has simply made the work too dangerous. In others, Russian strikes on fuel depots have left farmers unable to power their tractors.

Farmers accuse Russian forces of regularly targeting their grain silos and seizing their grain stores, particularly in the south.

And perhaps most frightening are the countless mines left by retreating Russian forces, especially in the north. The Ukrainian Deminers Association, a group that locates and removes explosives, says nearly 45 percent of the fields it has inspected in the Kyiv and Chernihiv regions were mined.

Gordie Siebring, a farmer based near the Belarusian border, said Ukrainian military authorities warned him he could not sow the fields closest to the frontier because of the mine threat, meaning he has been unable to plant 8 to 10 percent of his field. Neighboring farmers have it much worse, he said, because Russian mines have made over two-thirds of their fields too dangerous to use.

“If they are as close as 10 to 15 kilometers away, they can launch mines with artillery,” he said. “These mines have small parachutes and land in the fields and have sensors that cause detonation later. Those are really causing havoc.”

Another threat to global supplies, experts say, is that countries will hoard their own food stocks. Robert Habeck, the vice chancellor and minister of economic affairs of Germany, said countries should curb their use of grain to make biofuel and to feed livestock.

“Markets have to stay open,” Mr. Habeck said in an interview. “The worst thing that can happen now is that every country cares for its own supply, saves all the wheat, saves all the food, and does not give it to the market, because then we have no chance of securing the food supply.”

Before the war, droughts in North America and the Horn of Africa, poor harvests in China and France, and the pandemic were already squeezing food supplies, leaving the world uncommonly vulnerable. By December, global wheat prices had risen about 80 percent in a little over a year, according to the International Monetary Fund.

Even before Russian tanks rolled across Ukraine’s border, experts were warning of “a massive surge in food insecurity and the threat of famine,” said Adam Tooze, director of the European Institute at Columbia University.

The war, he said, is “impacting an incredibly fragile food system.”

At the same time, the spike in oil and gas prices caused by the war has triggered an even sharper increase in the cost of fertilizers made in part from those fuels.

Ms. von der Leyen said E.U. countries were increasing their own grain production and working with the World Food Program to ship available stocks to vulnerable countries at affordable prices.

“Global cooperation is the antidote to Russia’s blackmail,” she said.

Mark Landler, Matina Stevis-Gridneff and Patricia Cohen reported from Davos, Switzerland, and Erika Solomon from Lviv, Ukraine. Reporting was contributed by Carlotta Gall from Sievierodonetsk, Ukraine; Edward Wong from Washington; Matthew Mpoke Bigg from Krakow, Poland; and Monika Pronczuk from Brussels.