Kozlovskis announced the move on January 3 without explaining the reason for the decision.
Kozlovskis said Latvia in 2017 had blacklisted 100 people for different reasons, including an 'unfriendly attitude' toward Latvia and its people.
Kurlayev was detained and deported from Latvia after he arrived in Riga on January 1.
Kurlayev later told Russia's Channel One TV that Latvian authorities presented him with a document signed by the interior minister declaring that he had been banned from entering Latvia since 2015.
According to Kurlayev, the situation might be linked to a documentary he produced called NATO At The Gates, which included material he had gathered in Latvia in 2015.
Tensions between Russia and the former Soviet republics in the Baltics -- Latvia, Lithuania, and Estonia -- have increased since Russia's seizure and illegal annexation of Ukraine's Crimean Peninsula in 2014.
All three Baltic states are now members of NATO and the European Union.
Based on reporting by Delfi.lv and Kriminal.lv