As many as 4,000 migrants are camped out in the border area, while others are stuck on the Lithuanian border in freezing conditions, Polish authorities said.
Last week, the European Union accused Belarus of manufacturing the crisis to put political pressure on the bloc, amid escalating tensions with the government of Alexander Lukashenko.
Europe accuses Mr Lukashenko of rigging elections and committing human rights violations and in the latest crisis, launching a "hybrid attack" to destabilise the bloc by sending migrants to the border en-masse.
Mr Lukashenko has threatened to cut gas supplies to Europe, causing alarm in the EU.
Russian President Vladimir Putin, a close ally of the Belarus president, said that he’d talk to Mr Lukashenko and that any disruption in gas supplies would threaten the countries’ relationship as transit partners. Pipelines crossing Belarus are owned by Russia’s Gazprom PJSC, which lessens the risk of any shutdowns.
“Theoretically, Lukashenko, as the president of a transit country, can probably give instructions to cut off our supplies to Europe, although this would be a violation of our transit contract,” Putin said. “I hope it doesn’t come to that.”
Meanwhile, Mr Lukashenko said he wants Russian nuclear-capable Iskander missile systems to be deployed in the south and west of the country, he told a Russian defence magazine published on Saturday.
"I need several divisions in the west and the south, let them stand [there]," he said.
The Iskander mobile ballistic missile system, which has a range of up to 500 kilometres and can carry either conventional or nuclear warheads.
Russia's Defence Ministry has not made any comment on the matter.
Worries are mounting as thousands of asylum seekers attempt to cross into Europe via rugged countryside in the snow and rain.
At least eight have already died and fears are growing for the safety of others as harsh winter conditions set in.
The body of a young Syrian man was found in Poland near the Belarus border, Polish police said on Saturday.
"A forest worker informed the police about finding the body of a young man," Podlaska police spokesman Tomasz Krupa told Reuters, adding that the body and the man's passport had been found on Friday.
"It is a young man of Syrian nationality around 20-years old," Krupa said. It was not possible to determine the cause of death at the scene, he added.
On Saturday, the Polish army published footage that it said showed a group of about 50 migrants being escorted across the border by Belarusian forces.
The Polish Border Guard said Belarusian soldiers had pulled down a section of the temporary border fence.
In Lithuania, border guard officials released footage showing 70 migrants they said had been brought to the country's border by Belarusian officials in trucks.
"Upon arrival they are being pushed to the border and forced to make an illegal entry into the European Union," said Peter Stano, an EU spokesman.
Belarus claims the asylum seekers – most of whom are from Syria, Iraq and Kurdish-majority areas in both countries – are fleeing regional conflicts instigated by the West.
That view was supported by Mr Putin. "Let's not forget where these crises with migrants came from. Is Belarus a pioneer in these problems? No, the reasons were created by Western and European countries themselves," the Russian leader said.
Russia, the US and a number of European countries still have soldiers deployed in Syria and Iraq following a wave of regional instability which gave rise to ISIS.
Poland has deployed around 15,000 troops to the border area, while Belarus and Russia have held joint military exercises in response.
"We think it's a great concern. We communicated our concern to Russia, we communicated our concern to Belarus," Mr Biden told reporters as he departed the White House for a weekend at the Camp David presidential retreat on Friday. "We think it's a problem."
Mr Biden's remarks came hours after Vice President Kamala Harris voiced similar concerns during a visit to France, where she said she discussed the issue with President Emmanuel Macron.
Belarus "is engaged in very troubling activity. It is something that I discussed with President Macron, and the eyes of the world and its leaders are watching what is happening there," she told a news conference.
Belarus denies fomenting the crisis but has said it cannot help resolve the matter unless Europe lifts sanctions. The EU imposed several rounds of measures in response to Mr Lukashenko's violent crackdown on mass street protests against his rule in 2020.