Russia's presidential office says President Vladimir Putin sent a congratulatory message to Iranian President-elect Masoud Pezeshkian on Saturday.
Putin wrote that "Russian-Iranian relations are of a friendly, good-neighborly nature," and that the two nations "effectively coordinate their efforts to resolve topical issues on the international agenda."
He added, "I trust that your work as president will contribute to further enhancing constructive bilateral cooperation ... in the interest of strengthening regional security and stability."
Russia is said to have been buying weapons from Iran, including drones, since it started its invasion of Ukraine.
Putin apparently wants to boost military ties after the reformist president, who attaches importance to dialogue with Europe and the United States, takes office.
China's state-run media say Chinese President Xi Jinping sent a congratulatory message to Pezeshkian on Saturday.
Xi said that, in the face of the complex regional and international landscapes, China and Iran have always supported each other.
He added he attaches great importance to the development of China-Iran relations and is willing to work with Pezeshkian to guide the deepening of their comprehensive strategic partnership.
With its prolonged rift with the US in mind, China is keen on promoting multipolarization. It is strengthening its links with Iran, which has been at loggerheads with Europe and the US under the conservative hardline government.