"We have an interest in an EU that's united and prosperous, since the EU is our most important commercial and economic partner," Putin told Austria's ORF television a day before an official visit to Vienna.
"The more problems at the heart of the EU, the more risks and problems there are for us. We need to build cooperation with the EU," he said.
"We don't have a goal of dividing anything or anyone in the EU."
Putin, who was recently re-elected to a fourth Kremlin term, also played down reported links between his United Russia party and Austria's far-right Freedom Party (FPOe), which is now part of the governing coalition in Vienna.
Austria was one of the few EU nations not to expel Russian diplomats following the poisoning of ex-spy Sergei Skripal and his daughter Yulia in Britain in March.
Putin will meet Austrian President Alexander Van der Bellen as well as Kurz on Tuesday.