WASHINGTON, Aug. 21 -- When Russia's Ministry of Internal Affairs added Conor Kennedy's name to its international wanted list last week, it did more than open a criminal file on a 32-year-old American who had traveled to Ukraine to fight. It demonstrated that Moscow is prepared to pursue members of America's most recognizable political families through the same legal apparatus it has applied to hundreds of foreign nationals who chose to take up arms against Russian forces.

Kennedy, the grandson of Senator Robert F. Kennedy Sr. and the son of former U.S. presidential candidate Robert F. Kennedy Jr., was placed on Russia's federal wanted persons registry over allegations of mercenary service in the Ukrainian armed forces, according to Russ...