Meanwhile, Iraq Airways said it will carry out a repatriation flight to bring Iraqis stuck on the Belarus-Poland border back home.
Migrants who have spent days in a makeshift camp on the Belarusian side of Poland's eastern border are being taken away by bus by Belarusian officials.
The statement came from a Polish government official on Wednesday.
“I have received information that Lukashenko has provided the first buses which migrants are boarding and leaving,” Maciej Wasik, a deputy interior minister, said. “The camp site near Kuznica is slowly emptying."
It was not clear where they were being taken, and the information provided by officials is hard to verify due to restrictions journalists face in working on both sides of the border.
A state of emergency in Poland is keeping journalists, human rights workers and others away from the border along a zone that is 3 kilometers (2 miles) long.
The Belarusian state news agency Belta, on the other hand, reported that migrants were being given shelter inside a logistics center at the border, giving them the chance after many days to sleep indoors rather than in tents outdoors.
Belarusian and Polish border guards said on Wednesday around 2,000 migrants remained at the fence.
Iraq Airways will carry out a repatriation flight on Thursday to bring Iraqis stuck on the Belarus-Poland border back home, the national flag carrier said.
Tensions spiked on Tuesday as Polish forces at the border used water cannons and tear gas against stone-throwing migrants.
Warsaw accused Belarusian President Alexander Lukashenko's administration of giving smoke grenades and other weapons to those trying to cross the frontier.
But on Wednesday Polish authorities said the situation had calmed down, and while they registered 161 attempts to cross Poland's border illegally, the large migrant camp at the Kuznica crossing – which is now closed – had fewer people.
Iraq has been appealing for its citizens to fly home, telling them the way into the EU is closed. The first flights are scheduled for Thursday.
The West has accused Lukashenko of using the migrants as pawns to destabilize the 27-nation bloc in retaliation for its sanctions on his authoritarian regime. Belarus denies orchestrating the crisis.