* Tillerson first CEO to greet Putin in Vladivostok
* ExxonMobil, Rosneft working in "challenging circumstances"
* To start drilling in Kara Sea 2014-15
VLADIVOSTOK, Russia Sept 6 (Reuters) - The head of ExxonMobil held up a partnership with Russia's Rosneft as a model for the rest of the world, lending international credibility to President Vladimir Putin at a time when his authoritarian style faces mounting criticism.
ExxonMobil's Rex Tillerson, flanked by Rosneft CEO Igor Sechin, was the first foreign CEO to greet Putin ahead of the Asia-Pacific economic summit held in the sea port of Vladivostok, nine hours by plane east of Moscow.
Putin, while still serving as prime minister before returning to the Kremlin for a third term in May, presided over ExxonMobil's deal to join forces with state-controlled Rosneft to drill for oil in Russia's offshore zones and tap "tight" oil reserves in Siberia.
ExxonMobil and Rosneft unveiled the offshore exploration partnership that could invest up to $500 billion in developing Russia's vast energy reserves in the Arctic and Black seas in New York in April.
Under the deal Exxon and Rosneft will seek to develop three fields in the Arctic with recoverable hydrocarbon reserves estimated at 85 billion barrels in oil-equivalent terms.
"For the world, the political leadership, policy partnerships that have made our relationship possible serve as a model illuminating the path to a better future," Tillerson told Putin during a presentation.
"For Russia this relationship is already bearing fruit in terms of new investment, innovations, new possibilities," Tillerson said.
ExxonMobil's expansion into Russia is taking place amid new uncertainty in relations between the two Cold War foes following Putin's return to the Kremlin and ahead of the U.S. presidential election.
Putin has also faced growing opposition at home as tens of thousands of people took to the streets of Moscow and other large cities with allegations of ballot fraud after last December's parliamentary election and some investors are worried about signs of a crackdown.
The U.S. government joined European nations in openly criticising Russia for the jail sentences handed to three members of Pussy Riot, a punk band which protested against Putin in a church.
At the same time, Tillerson and other ExxonMobil executives have enjoyed an increasingly cozy relationship with Rosneft and the Kremlin, and mingled with Rosneft executives and Kremlin officials at a fuel storage facility outside Vladivostok's new airport.
He said ExxonMobil and Rosneft will work in "challenging circumstances" seeking to meet the growing global energy demand which he expects to grow by 30 percent by 2040.
Tillerson said seismic studies at the Arctic Kara Sea oil exploration project with Rosneft were ahead of schedule and he expected drilling to commence in 2014-15.
"With this data on the Kara Sea in hand and analysed we expect the drilling of an exploration well in the 2014-15 time frame," he said.
Tillerson said he saw potential for exploration drilling in the Black Sea also in 2014-15. Sechin said he hoped the drilling in the Kara Sea will start in 2014.
Putin, who has repeatedly said that increased trade and closer economic ties were key to improving the broader relationship with the U.S., listened carefully, asking in the end how ExxonMobil would ship oil extracted in the Kara Sea.
"We will undertake a study of a couple of different alternatives, most likely through the north west, through some of the shipping lanes whose current activity is shipping minerals from the mines in the area," Tillerson said.
"It may be piped to the shore, to the terminal," he said, adding a decision would depend on where oil was found.