The court refused to uphold the appeal filed by Kasem's lawyers.
The defense plans to file a complaint with the European Court of Human Rights.
Earlier, the official representative of the Russian Foreign Ministry, Maria Zakharova, said that the detention of Kasem in Latvia is persecution for political reasons.
On January 5, Marat Kasem was detained by Latvian special services in Riga on suspicion of violating EU anti-Russian sanctions and espionage.