Bekjanov, the former editor of an opposition newspaper in Uzbekistan, was arrested in 1999. The charges were related to the publication of the newspaper and to alleged participation in banned political activities.
He was originally sentenced to 13 years, but had another five years added to his sentence for unspecified violations of prison rules.
In a statement on its website, a Central Asia researcher from Human Rights Watch, Steve Swerdlow, called on President Shavkat Mirziyoyev to "allow Bekjanov to travel to the US to join the rest of his family."
Bekjanov's daughter lives in the United States.
At the time of Bekjanov's arrest, Uzbekistan was ruled by Islam Karimov, an authoritarian ruler who was in power for nearly 27 years until his death in 2016.
After his death, some of Karimov's political enemies have been released from prison, but observers do not believe there will be a significant shift in the political environment under Mirziyoyev. Mirziyoyev was elected with a supposed 88.7 percent of the vote in December 2016.
mz/msh (AFP, Reuters)