13 July 2015, 12:05 GMT
“The NSC Twitter account is under Right Sector control,” one message read.
“General Taran provides cover for illegal smuggling in the Anti-Terrorist Operation Zone,” said another.
The NSC’s Twitter account earlier featured a post about General Taran having been fired as the federal government’s representative at the Joint Ceasefire Monitoring Center in Donbass on suspicion of high treason.
13 July 2015, 07:05 GMT
The hack comes amid Right Sector protests in several Ukrainian cities, including Kiev and Lviv, following a police shootout involving its members in the Ukrainian southwestern city of Mukachevo.
The Right Sector is a loose assembly of radical nationalist organizations that played a major role in violent clashes leading to the February 2014 coup in Ukraine.
In November 2014, the Russian Supreme Court recognized the Right Sector as an extremist organization, and its activity was subsequently banned in Russia. In Russia, a criminal case has been launched against the group for its terrorist activities.