Russia however was "deeply convinced that the proliferation of nuclear arms on the planet does not contribute to security either for the region or the world," Putin said.
"We hope that Iran will strictly respect all commitments its has made bilaterally with Russia and internationally," the Russian president stated.
Rowhani said Russia had a role of "great importance" to play in resolving the dispute over Iran's nuclear program.
Putin said he had been invited by the Iranian leadership to visit Tehran and was "preparing for this visit," Interfax news agency reported.
Dates for Putin's trip to Iran would be set later, he said.
Putin's meeting with Rowhani came a day after both countries announced that a crucial agreement obliging Iran to return all spent nuclear fuel to Russia would be signed on February 26.
An agreement on the return to Russia of spent nuclear fuel has been the key impediment to completion of an 800-million-dollar project led by Russia to build the plant in Bushehr, southern Iran.
Moscow and the West both fear Iran could reprocess the spent fuel delivered from Russia by upgrading it through centrifuges to either make a weak "dirty bomb" or an actual nuclear weapon.
The United States and Israel had jointly launched an international campaign against the Bushehr project, but Moscow countered that it would make sure the plant remained harmless to protect its own security interests.
Tehran has in the past used various arguments to avoid signing the agreement. It has said the material was too volatile and dangerous to transport back to Russia and also that Moscow was charging too much for the fuel itself.
The United States accuses Iran of using atomic energy as a cover for weapons development, a charge Tehran denies.