MOSCOW (AFP) - Russian President Vladimir Putin on Sunday congratulated Mr Hassan Rohani on his victory in Iran's presidential election and urged him to forge closer ties with Moscow.

"Putin expressed confidence that Hassan Rohani's work on this high post will promote the flourishing of (Russian) friend Iran and further strengthen Russian-Iranian relations," the Kremlin quoted Mr Putin as saying in a message to Iran's president-elect.

"The Russian president also confirmed his readiness to advance the development of mutually beneficial cooperation with Iran in various fields, in the interests of regional security and international stability," the Kremlin statement said.

Moderate cleric Rohani was declared Iran's new president on Saturday in an outright election victory that ends an eight-year conservative grip on the top office.

Mr Rohani, 64, a former top nuclear negotiator who has championed more constructive engagement with world powers, won outright in the first round with 50.68 per cent of votes cast.