Koktysh has been detained for more than two years for the peaceful expression of his beliefs, Amnesty says. It considers him to be a prisoner of conscience.
It adds that Koktysh should not be forcibly returned to Belarus, where it says he may be at risk of the death penalty on fabricated charges.
Koktysh was detained in Ukraine after Belarus requested his extradition over what Amnesty calls a "baseless accusation" that he committed murder in Belarus in January 2001.
Koktysh was put on trial for murder in December 2001 after being held in detention for almost a year, during which time he was allegedly tortured and ill-treated. At his trial, he proved that he was in another city when the murder took place and was acquitted and released.
He moved to Ukraine and married. In 2007, Ukrainian authorities honored an extradition request after Belarus's Prosecutor-General appealed the verdict and a retrial ordered.
Koktysh's appeal for refugee status was denied by Ukrainian authorities.
Amnesty notes that a number of international human rights conventions to which Ukraine is a state party prohibit the deportation or extradition of anyone to a country where he or she may face the death penalty, torture, or other ill-treatment or other grave human rights violations.