LVIV, Ukraine (NewsNation) — The first convoy of civilians to evacuate embattled Ukrainian cities along safe corridors began Tuesday, amid the U.N. officials’ announcement that the exodus of refugees from Russia’s invasion reached 2 million.

Video posted by Ukrainian officials showed civilians began leaving in buses moving along a snowy road from the eastern city of Sumy heading toward the southern port of Mariupol.

As the cross-border exodus from Ukraine continued, the humanitarian situation in the country’s besieged cities grew grim, including the port of Mariupol, where bodies lay uncollected in the streets and civilians waited anxiously for word that they’d be allowed to evacuate.

Ukraine’s government accused Russia of shelling a humanitarian corridor it had promised to open to let residents flee Mariupol.

“We have already started the evacuation of civilians from Sumy to Poltava (in central Ukraine), including foreign students,” the foreign ministry said in a tweet. “We call on Russia to agree on other humanitarian corridors in Ukraine.”

Previous attempts to lead civilians to safety have crumbled with renewed attacks. It was not clear how long the efforts would last.

The temporary cease-fire between the forces of Moscow and Kyiv was declared on Tuesday to evacuate civilians from five major cities in Ukraine including the capital.

Russia’s coordination center for humanitarian efforts in Ukraine and Ukrainian Deputy Prime Minister Iryna Vereshchuk both said a cease-fire was agreed to start Tuesday morning to allow some civilians to evacuate, but it was not clear where all the corridors would lead to, amid disagreement between the two sides.

Russia’s coordination center suggested there would be more than one corridor, but that most would lead to Russia, either directly or through Belarus. At the U.N., however, the Russian ambassador suggested corridors from several cities could be opened and people could choose for themselves which direction they would take.

Vereshchuk said 30 buses were sent from Zaporizhzhia to Mariupol with humanitarian aid, including water, basic food staples and medicines, and will be used to bring out civilians.

Ukrainian President Volodymyr Zelensky shared a video message in Kyiv on Tuesday morning following the temporary cease-fire

“We will fight till the end at sea, in the air. We will continue fighting for our land, whatever the cost,” he said. “We will fight in the forests, in the fields, on the shores, in the streets” and even on the banks of rivers.

Speaking by video from Ukraine and wearing army green, Zelenskyy thanked Britain for its support, which includes humanitarian aid and defensive weapons. He urged the U.K. to increase sanctions on Russia, to recognize Russia as “a terrorist country” and to keep Ukraine’s skies safe.

Zelenskyy also thanked President Joe Biden via Twitter for “striking in the heart of Putin’s war machine and banning oil, gas and coal from US market.”

Biden on Tuesday announced a ban on U.S. imports of Russian oil, the latest sanction intended to punish Moscow for its invasion of Ukraine.

Biden’s announcement came amid rising pressure from Democrats and Republicans, and it reflects a willingness to accept the political risk of rising gas prices to economically retaliate against Russia.

“Defending freedom is going to cost,” Biden said. “It’s going to cost us as well in the United States.”

The U.S. believes Russia underestimated the strength of Ukraine’s resistance that has likely caused thousands of Russian casualties, the Biden administration’s top intelligence official told lawmakers Tuesday.

The testimony, in a hearing before the House Intelligence Committee, amounted to the first public disclosure by the nation’s most senior intelligence officials about how the war is proceeding.

NATO Secretary-General Jens Stoltenberg said Tuesday that Russia’s armed forces may be deliberately targeting civilians as they try to flee the military assault on Ukraine.

“There are very creditable reports of civilians coming under fire as they try to evacuate. Targeting civilians is a war crime, and it’s totally unacceptable,” Stoltenberg said.

He told reporters in Latvia that the humanitarian impact of the almost two-week-long war “is devastating.”

“We need real humanitarian corridors that are fully respected,” he said.

The Russian onslaught has trapped people inside cities that are running low on food, water and medicine amid the biggest ground war in Europe since World War II. And evacuations are taking place amid magnified fears of an intensifying humanitarian crisis.

Jan Egeland, secretary-general of the Norwegian Refugee Council, said that refugees fleeing in Ukraine was “the fastest-growing displacement crisis I have witnessed in my 35 years as a humanitarian worker.”

The Oslo-based agency, which has been in Ukraine since 2014, said it was launching an aid plan to support 800,000 people inside Ukraine and neighboring countries.

The Office of the U.N. High Commissioner for Human Rights revealed in a statement on Monday that 406 civilians, including 27 children, have been killed and 801 others have been injured since the start of the war on Feb. 24. However, it said the real figure was likely to be much higher.

The U.N. Human Rights office said of the casualty count that the “real figures are considerably higher.” Ukraine’s emergency service has estimated the civilian death toll at more than 2,000.