"The US president had nothing to do with organizing the prisoner exchange between Russia and Western countries, although now he is trying to 'earn credibility on it,'" Lukashenko was quoted as saying by the Belarus Today newspaper.
He also said that the exchange was organized exclusively by the special services without any diplomats involved, with the Belarusian side providing as much assistance as possible.
The United States, Russia, Germany, and other Western countries have struck a deal for a 24-person prisoner swap, which is one of the largest prisoner exchange agreements since the end of the Cold War.
On Thursday, the Russian Federal Security Service said eight Russians detained and held in custody in a number of NATO countries had returned to Russia.
A Sputnik correspondent later reported that a plane carrying former US Marine Paul Whelan, Wall Street Journal reporter Evan Gershkovich and Russian-American journalist Alsu Kurmasheva landed at Joint Base Andrews, Maryland, late Thursday night.