Ukraine has accused Belarus of stoking tension over hundreds of Hasidic Jewish pilgrims stranded at their border.
The office of Ukraine's president said Belarus was spreading false hope that the pilgrims could cross. Belarus wants a corridor to be opened for them.
The pilgrims are trying to travel to the town of Uman for the Jewish New Year, to pay respects at the tomb of the founder of a Hasidic movement.
Ukraine has closed its borders to foreigners to limit Covid-19.
The restrictions apply from 28 August to 28 September.
Ukraine-Belarus relations soured after Ukraine joined the EU in refusing to recognise the re-election of Belarus President Alexander Lukashenko last month.
Israel, meanwhile, is the first country to impose a second nationwide Covid-19 lockdown - set to start on Friday - after a large spike in infections.
How did the situation arise?
Every year thousands of pilgrims, many of them from Israel, make the journey to Uman on Jewish New Year, which in 2020 runs from 18 to 20 September. They visit the tomb of Rabbi Nahman, the founder of the Breslov Hasidic movement.
The pilgrims set off despite calls from both the Ukrainian and Israeli governments for them not to travel this year because of coronavirus concerns.
Thousands are reported to be already in Uman.
But others travelling mostly via Minsk have been stopped at the Belarus-Ukraine border by Ukrainian guards. The numbers vary but some estimates put the figure at over 2,000 at various border points.
What have Ukraine and Belarus said?
The office of Ukraine's President Volodymyr Zelensky said: "We call on the Belarusian authorities to stop creating additional tension on the border with our country and not make false encouraging announcements for pilgrims, which could give them the impression that Ukraine's border could still be open to foreigners."
The head of the Ukrainian border guard service, Sergiy Deyneko, said more than 3,000 pilgrims could soon be at border points in the Chernihiv, Zhytomyr and Volyn regions.
The office of Mr Lukashenko accused Ukraine of "shutting its borders" and stranding hundreds.
On Tuesday he said there should be a "green corridor" so pilgrims could get to Uman on buses and then be ferried back to Belarus.
Ukrainian authorities said water and kosher food was being supplied but the Belarus Red Cross Society said the pilgrims did not have "enough resources to ensure their basic needs".
What are the pilgrims saying?
One stuck at the border, Haim Weitshandler, told Agence France-Presse it was a "humanitarian catastrophe", with "sick and hungry people" left out for days in the rain and cold.
"We are stuck here with no money, no roof, no food or drink," the 40-year-old said.
Pilgrims were resting at the side of the road, blocked off by border guards.
Some had set up makeshift tents, while others slept on their luggage in front of lorries.
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