Clinton failed to win specific pledges from Moscow for tougher sanctions against Iran during a visit to Russia last week, but she said in the interview that there was broad agreement with the Kremlin on how to proceed.
"We have agreed to make diplomacy the priority with Iran. But if we are not successful, we will consider other steps," Clinton said in the interview, which was conducted by Newsweek's Russian edition and appeared in German daily Die Welt.
She described her talks with Russian leaders as "very constructive" and said the two countries were in "full agreement" on the way forward.
Clinton also said it was positive that Russia had not followed through on plans to deliver high-grade S300 air defence missiles to Iran.
"Until now they have not delivered any rocket systems to Iran. We see this as a good sign," she was quoted as saying.
Her comments were translated from the German by Reuters because Die Welt was not immediately able to provide an English transcript.
Clinton also reiterated that Washington was ready to cooperate with Moscow on missile defence after U.S. President Barack Obama scrapped his predecessor George W. Bush's plan to put parts of an anti-missile system in eastern Europe.
"On the question of the missile shield, we are very open to cooperation with the Russians. We have made this clear to them. We believe that a joint missile defence would make sense," Clinton said.
(Writing by Noah Barkin)
