LVIV, Ukraine — Buses carried civilians out of an embattled Ukrainian city Tuesday along a safe corridor agreed to by the two warring sides, while a parallel effort to relieve the besieged port of Mariupol was thrown into jeopardy by reports of renewed Russian shelling.

Europe’s worst refugee crisis since World War II grew even more severe, with U.N. officials reporting that 2 million people have now fled Ukraine.

Moscow’s forces have besieged Ukrainian cities and cut off food, water, heat and medicine in a growing humanitarian crisis. But for days, attempts to create corridors to safely evacuate civilians have stumbled amid continuing fighting and objections to the proposed routes.

On Tuesday, a convoy of buses packed with people fleeing the fighting moved along a snowy road from Sumy, a northeastern city of a quarter-million people, according to video from the Ukrainian communications agency. Ukrainian Deputy Prime Minister Iryna Vereshchuk said they were headed southwest to the Ukrainian city of Poltava, and included students from India and China.

Hours before the convoy reached Sumy, overnight strikes killed 21 people there, including two children, Ukrainian authorities said.

Meanwhile, buses emblazoned with red cross symbols carried water, medicine and food toward the encircled southern port of Mariupol, scene of some of the worst desperation. Vereshchuk said the vehicles would then ferry civilians out of the city of 430,000 people.

But soon after officials announced that buses were on their way, Ukrainian officials said they had learned of shelling on the escape route.

It was unclear whether the supply convoy made it to Mariupol. And it appeared unlikely that civilians would be able to board the buses to get out.

The deputy mayor of Mariupol cast doubt on the evacuations, telling the BBC that Russian forces continued to pound areas where people were trying to gather ahead of being taken out. He said some roads were blocked, others were mined.

“So we cannot establish sustainable cease-fire and safety route at the moment,″ Serhiy Orlov said. “So we still have … a city in blockade.’’

The city is without water, heat, sanitary systems or phone service. Residents have been collecting water from streams or by melting snow. With the electricity out, many people are relying on their car radios for information, picking up news from stations broadcast from areas controlled by Russian or Russian-backed separatist forces.

Looting has become widespread for food, clothes and even furniture, with locals referring to the practice as a “discount.”

In a video address from an undisclosed location, Ukrainian President Volodymyr Zelenskyy said a child had died of dehydration in Mariupol, another sign of the city’s desperation.

Nearly two weeks into the fighting, Russian forces have captured a swath of southern and coastal Ukraine but have seen their advances stopped in many areas — including around Kyiv, the capital — by nimble Ukrainian fighters targeting Moscow’s armored columns.

Thousands of people are thought to have been killed, both civilians and soldiers, though the actual number remains unknown.

As the humanitarian disaster has unfolded, the fighting has caused global economic turmoil, with energy prices surging worldwide and stocks plummeting. The war threatens the food supply of millions around the globe who rely on crops farmed in the fertile Black Sea region.

Western countries have rushed weapons to Ukraine and moved to slap Vladimir Putin’s Russia with sanctions.

In a further effort to punish Russia, U.S. President Joe Biden decided to ban Russian oil imports, according to a person familiar with the matter who spoke on the condition of anonymity to discuss the matter before an announcement. Also, Shell announced will stop buying oil and gas from Russia.

Ukraine’s military said Ukrainian forces continued defense operations in the Mariupol suburbs. The military said “demoralized” Russian forces are engaging in looting, commandeering civilian buildings and setting up firing positions in populated areas. The claims could not be independently verified.

The battle for Mariupol is crucial because its capture could allow Moscow to establish a land corridor to Crimea, which Russia seized from Ukraine in 2014.

Oleksiy Kuleba, governor of the Kyiv region, said Ukraine was also making arrangements to get people out of the suburb of Irpin.

Late Tuesday, Zelenskyy released a selfie video of himself standing near the presidential offices in Kyiv, with piles of sandbags, a snow-dusted fir tree and a few cars in the background.

It was the second video in 24 hours showing him near the country’s seat of power, in an apparent bid to dispel any doubts over his whereabouts.

In a soft voice, he said: “Snow fell. It’s that kind of springtime. You see, it’s that kind of wartime, that kind of springtime. Harsh. But we will win.”