Chichiashvili is charged with kidnapping Spanish businessmen Antonio Tremino and Francisco Rodriguez and British banker Peter Shaw and other crimes.
Valery Khaburdzania and Georgian Prosecutor General Irakly Okruashvili arrived in Moscow on Wednesday morning.
Okruashvili is to spend some more days in Moscow to discuss with his Russian colleagues the detention and extradition to Georgia of Levan Mamaladze, the ex-governor of the Kvemo Kartli region. Mamaladze is charged with embezzlement and financial machination.
On Wednesday Valery Khaburdzania and Irakly Okruashvili met with Russian Prosecutor General Vladimir Ustinov. They discussed this issue and detentions and extraditions to Georgia of its citizens who shelter in the Russian Federation.