"I think that the only way Europe could regain at least half of its losses in competitiveness is to build pragmatic cooperation with Russia," Szijjártó said at a news briefing at UN Headquarters in New York.
"It is in Europe's interests to be able to restore pragmatic cooperation with Russia."
Russia's relations with the European Union and their allies deteriorated sharply in 2014 over the Ukrainian crisis.
Europe is currently struggling to manage a massive migration crisis with some 500,000 asylum seekers arriving in the bloc since the beginning of 2015, according to European Commission estimates.
Russia will join the discussion on migration policies at the 4th International Parliamentary Forum held from October 1 in Moscow.