Speaking to Reuters via Skype, Linas Antanas Linkevicius also said EU sanctions are possible against Belarus officials who used force against peaceful protesters.
"Crackdown in Belarus after the election is unacceptable and we cannot tolerate it and there should be some political consequences," Linkevicius added.
Tikhanouskaya, who has Lithuanian visa and can stay in a Baltic stay for up to a year, said on Tuesday she had fled abroad for the sake of her children, after two nights of clashes following the contested re-election of strongman President Alexander Lukashenko.
Both she and the Belarusian authorities said she had not been forced to leave.
There had been concern about Tikhanouskaya's whereabouts after her campaign team said on Monday they had been unable to reach her by phone hours after she was known to have left a meeting with central election commission officials.
At least one person died as police clashed with protesters on Monday (August 10) after the opposition accused Lukashenko of rigging the vote amid widespread criticism from Western leaders.
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LINAS ANTANAS LINKEVICIUS: [INAUDIBLE] she-- together with a lawyer, she visited the electoral committee to submit complaint about the counts of the votes. And she stayed for a very long time. Lawyer left the building, but she stayed longer. And it lasted around seven hours, totally.
So we didn't know where she is and what she's doing. And then I informed that I cannot reach and cannot find. So it was-- all night what kind of tension. Then, I understand that she had not so many options just to leave the country. She had our national visa, and it was her decision to leave to Lithuania.
So authorities didn't prevent this [INAUDIBLE] from happening. And then the nighttime [INAUDIBLE] in the morning hours, she arrived in Lithuania. So she is in Lithuania. She is safe.