The other two council members, press secretary Anton Rodnenkov and executive secretary Ivan Kravtsov, told a press conference in Kiev that Kolesnikova had torn her passport "into small pieces" and climbed out of the back window of the auto to avoid expulsion.
The Associated Press reported that earlier in the day, the dissenters were driven to the Ukrainian border, where the authorities told them to cross over to Ukraine.
Ukrainian border guards said that Kolesnikova had not entered the country, refuting initial claims that she had crossed the border.
"And now, we, including Maria Kolesnikova, will cross the border of the Republic of Belarus and will leave it for the time being", Kravtsov said in the video.
Lukashenko told Russian media Tuesday that Kalesnikava was arrested after being pushed out of their auto as the three members of the unified opposition's coordination council tried to flee Belarus illegally during the night.
Anton Bychkovsky, spokesman for Belarus's Border Guard Committee, confirmed that Kolesnikova is in the custody of Belarusian authorities, but refused to give any details of what happened on the border. Kravtsov's auto was waiting for them in the neutral territory between the two nations' checkpoints and the men were placed inside the vehicle.
Fellow Coordination Council member Pavel Latushko, who himself is in Poland, told Russia's TV Rain he "received information from the Coordination Council that Maria ripped her passport while crossing the border".
The Coordination Council is a seven-member presidium created by Ms Tsikhanouskaya that aims to coordinate a peaceful and orderly transfer of power from Mr Lukashenko, and to hold new presidential elections.
FILE- Maria Kolesnikova one of Belarus opposition leaders gestures during a rally in Minsk Belarus Aug. 30 2020
Viktoria Tsepkalo, presidential candidate Svetlana Tikhanovskaya, and Maria Kolesnikova, have united together to challenge Mr Lukashenko's presidency.
Friends of the 38-year-old had been unable to contact her after she was allegedly snatched by masked men who bundled her into a van on Monday, a claim which Belarus denies.
Amid Western criticism, Lukashenko has relied on support from Moscow, his main sponsor and ally.
The Lithuanian foreign minister, Linas Linkevicius, has urged the bloc to provide "concrete help" to Belarus's opposition and said "the Belarusian people should not feel deserted". Lukashenko assumed that Kravtsov and Rodnenkov who drove a vehicle just "tossed" their associate, one of the opposition leaders Mariya Kolesnikova out of the auto.
"I won't talk to the opposition's Coordination Council because I don't know who these people are".
"If Belarus falls, Russian Federation will be next".
Speaking to reporters from her apartment, she said she doesn't plan to leave the country despite the official pressure.
Despite Lukashenko's hard-headed tactics against opposition figures, and arrests of at least 7,000 protesters up to date, tens of thousands of people have still shown up in the streets of Minsk to protest the state's suppressive policies at the weekend.
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