"Our relations with Hungary, despite the current problems with the European Union, remain stable and friendly," Medvedev stressed after hosting his colleague.
The Hungarian prime minister outlined Budapest’s aspiration to maintain "all that is good" in relations with Russia "despite all the difficulties."
"In terms of peace and other issues, Hungary will remain Russia’s good partner," Orban added.
The Central European nation is one of a handful EU members that oppose the expansion of anti-Russia sanctions imposed by the 28-bloc along with the United States and other Western states.
Sunday marks the last day of the 16th FINA World Championships hosted by the capital of Russia’s Republic of Tatarstan, which kicked off on July 24. Hungary hosts the next global swimming competition in 2017.