"As far as I know, the cats have not joined any party or faction. Getting them involved politically is impossible," said Turlais.
"They are not part of any opposition party. May the tiny creatures live on and bring us joy," he said.
Kuzja and Muris are living in the mayor's office since late 2011 after Ušakovs adopted them from an animal sanctuary.
Turlais, supported by coalition parties Harmony and Honor to Serve Rīga, is expected to become the Latvian capital's new mayor on May 30.