Ali Larijani made the comments during a meeting with Konstantin Shyulavov, the Russian representative at the Non-Aligned Movement summit in Tehran, RIA Novosti reported.
"The two countries share many interests and common views in international fields that can serve as a basis for constructive cooperation between Tehran and Moscow," Larijani said.
He said the Majlis, Iran's parliament, would do its best to promote "amicable ties" with Russia.
Larijani said Iranian and Russian officials should consult with each other on common stances on key international issues, Iran's Press TV reported.
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