A Ukrainian press freedom organization, the Institute of Mass Information, is also expressing fears that Klymentyev may be dead after his mobile telephone reportedly was found on a boat in the region of Kharkiv.
Klymentyev is the editor in chief of the "Novyy Styl." The small investigative newspaper focuses on corruption issues in Kharkiv and is known for Klymentyev's criticism of law enforcement officials.
The Associated Press reports that Klymentyev was threatened after refusing to accept money to hold back a story about a regional prosecutor accused of accepting bribes to close criminal cases.
Ukraine's President Viktor Yanukovych said last week that he would personally oversee an investigation into Klymentyev's disappearance.