* Moscow plays to Iran, West with plant start-up
* Persistent tension ensures Russia diplomatic role
* Part of push for nuclear energy riches
(Corrects month in paragraph 6 to June instead of April)
By Steve Gutterman
MOSCOW, Aug 21 (Reuters) - For Russia, Iran's first nuclear power plant is a project in which everybody wins -- a statement some in Israel, the United States and elsewhere would vehemently dispute.
What's clear is that Moscow has little to lose from the start-up of the Bushehr plant, set in motion on Saturday 15 years after Russia agreed to build the reactor at a site left idle following Iran's 1979 Islamic Revolution.
For the Kremlin, launching the long-delayed power plant bolsters Russia's aggressive campaign to capture nuclear energy markets abroad and underscores its position at the heart of global diplomacy over Iran's nuclear programme.
But it will not end tension over Tehran's ambitions or silence the talk of an attack on Iran -- factors that help fuel Russia's economy by bolstering the price of oil, a major source of revenue.
Russia continues to strike a delicate balance, playing to oil-rich Iran's insistence on a need for nuclear power and at the same time to Western worries that Tehran could develop an atomic bomb.
Starting the plant is a way for Moscow to appease Tehran after pleasing the U.S. administration by approving fresh U.N. sanctions against Iran in June and vowing not to send it air-defence missile systems while the measures are in place.
The United States criticised Moscow earlier this year for pushing ahead with start-up plans amid persistent Iranian defiance over its nuclear activities, which Washington fears are aimed at acquiring weapons.
But the mandatory return of Bushehr's spent fuel to Russia allows Moscow to cast the plant as a model for proliferation risk-free nuclear cooperation.
Because weapons-grade plutonium can be derived from spent fuel, Bushehr -- which the United States for years appealed to Russia to scrap -- now also hands the West an argument that Tehran has no need to enrich uranium itself.
Iran, though, insists it has the right to enrich uranium and refuses to suspend its enrichment efforts.
A day before Saturday's start-up ceremony, Iranian President Mahmoud Ahmadinejad was quoted as saying in a Japanese newspaper that Iran would stop higher-grade enrichment if it were assured of fuel supplies for a research reactor separate from Bushehr.
Russia suggested it was ready to entertain the offer, calling for a meeting as soon as possible on potential deliveries of the fuel.
But with no clear resolution in sight, the United States and Europe will continue to need the support of Russia -- which is cementing its Iranian ties by delivering on Bushehr -- in its efforts to rein in Tehran's nuclear programme.