Sviatlana Tsikhanouskaya initially refused to concede defeat in the election amid a massive police crackdown on protesters.
Looking dishevelled and distressed, Ms Tsikhanouskaya, a former teacher and political novice, apologised to her supporters in a video statement and said it was her own choice to leave the country.
She said: “It was a very hard decision to make. I know that many of you will understand me, many others will condemn me and some will even hate me. But God forbid you ever face the choice that I faced.”
In a later video statement, she urged her supporters to respect the law and avoid clashes with police.
Her campaign aides said she made the unexpected move under duress. Ms Tsikhanouskaya’s husband has been at a Belarusian jail since his arrest in May.
Maria Kolesnikova, a top figure in Ms Tsikhanouskaya’s campaign, said: “It’s very difficult to resist pressure when your family and all your inner circle have been taken hostages.”
Ms Tsikhanouskaya previously dismissed the official results of Sunday’s election showing authoritarian President Alexander Lukashenko winning a sixth term by a landslide. Thousands of opposition supporters who also protested against the results met with a tough police crackdown in Minsk and several other Belarusian cities for two consecutive nights.
On Monday, a protester died during the clashes in Minsk and scores were injured as police used tear gas, flash-bang grenades and rubber bullets to disperse the demonstrators. The Interior Ministry said the victim intended to throw an explosive device, but it blew up in his hand and killed him.
The ministry said more than 2,000 people were detained across the country for taking part in unsanctioned protests on Monday evening and overnight. It added that 21 police officers were injured in clashes with protesters, and five of them were admitted to hospital.
The previous day, the Interior Ministry reported more than 3,000 detentions and said that 89 people were injured, including 39 law enforcement officers.
Ms Tsikhanouskaya, a 37-year-old former English teacher without any prior political experience, entered the race after her husband, an opposition blogger who had hoped to run for president, was arrested in May. She has managed to unite fractured opposition groups and draw tens of thousands to her campaign rallies – the largest opposition demonstrations in Belarus since the 1991 collapse of the Soviet Union.
In the video statement posted on her Facebook page, Ms Tsikhanouskaya thanked her supporters for backing her candidacy, but added that “the people of Belarus have made their choice”.
“Belarusians, I’m urging you to show common sense and respect for the law,” she said, reading a text without raising her eyes from the paper. “I don’t want blood and violence. I’m asking you not to confront the police and not take to squares to put your lives in danger. Take care of yourselves and your relatives.”
Hours before that, Ms Tsikhanouskaya disputed the vote results and submitted a formal request for a recount to the Central Election Commission. She stayed in the commission headquarters for hours and faced senior law enforcement officers, according to her campaign aides.
One aide, Olga Kovalkova, said the U-turn came following pressure from the authorities who made Ms Tsikhanouskaya read a prepared statement and then drove her out of the country.
Ms Kovalkova said: “We don’t know what kind of pressure she was subjected to and how they tried to break her. She couldn’t have said it on her own. She was reading a prepared text.”
She said Ms Tsikhanouskaya left the country with her campaign chief, Maria Moroz, who had been detained over the weekend. Several other campaign aides have remained in custody.
Mr Lukashenko, who has ruled the ex-Soviet nation of 9.5 million with an iron fist since 1994, derided the opposition as “sheep” manipulated by foreign masters and vowed to continue the tough crackdown on protests despite rebukes from the West.
Election officials said Mr Lukashenko won a sixth term in office with 80% of the vote, while Ms Tsikhanouskaya got 10%.
When asked on Monday if she was planning to go abroad to avoid being arrested, Ms Tsikhanouskaya said she had no such plan and saw no reason why she would be arrested.
But after submitting her formal demand for a recount to Belarus’ Central Election Commission, she told her allies: “I have made a decision, I must be with my children.”
Speaking in the video statement from Lithuania, she emphasised that “children are the most important thing in our lives” and conceded her weakness.
“I thought that the campaign had tempered me and make me so strong that I could resist anything,” she said. “But it appears that I have remained the same weak woman that I was before.”