UPDATE 3-BP holds talks with Russian partners amid row

(Adds Vekselberg in para 3, 13-14)

By Ekaterina Golubkova and Guy Faulconbridge

MOSCOW Jun 6 (Reuters) - BP (BP.L) Chief Executive Tony Hayward held talks with a Russian shareholder of BP's local venture on Friday after an outbreak of public sparring between the partners amid speculation the Russian side could sell out.

A BP spokesman said Hayward had met TNK-BP shareholder Mikhail Fridman, describing the talks as "positive" and adding they would continue to try and resolve their differences.

Fridman's partner and another major Russian shareholder Viktor Vekselberg said he expected the dispute to be resolved within days, while sources close to the Russian shareholders said the parties would meet again in three days.

Hayward, whose firm owns half of the third-largest Russian oil producer, flew to Moscow on Thursday to discuss the future of the embattled company, which many analysts expect to fall under the control of a Russian state firm.

BP and TNK-BP's Russian shareholders, who split control of TNK-BP 50-50, last week publicly confirmed they had differences over the company's strategy for the first time. Every fourth barrel of BP's production comes from Russia.

A source close to TNK-BP said Hayward had also met Fridman's partners in the Alfa Group conglomerate, German Khan and Peter Aven, as well as Deputy Prime Minister Igor Sechin.

"Positive developments were evident," a source close to TNK-BP told Reuters.

The Russian owners -- Fridman, Khan, Vekselberg and Len Blavatnik -- have demanded the resignation of TNK-BP Robert Dudley. But he, with the backing of BP, has resisted calls to step down.

On Thursday, Hayward held talks with Alexei Miller, the CEO of state-controlled gas major Gazprom (GAZP.MM), Sechin, who is also the chairman of oil major Rosneft (ROSN.MM), and first deputy premier Viktor Zubkov, who is poised to become chairman of Gazprom later this month.

Also on Thursday, TNK-BP said an Interior Ministry department had issued a summons to Dudley as part of a tax probe for 2001-2003.

The summons came on top of other TNK-BP problems including the arrest of an employee on an industrial espionage charge, a raid on the company's central Moscow offices and a court injunction to stop it using BP specialists.

Analysts have said the pressure was inspired by the Kremlin, which, eager to regain control over the strategic energy sector, wanted to have a state company such as Gazprom take over a stake in TNK-BP.

Russian shareholders have repeatedly denied plans to sell out and Vekselberg again repeated on Friday the sale was not on the agenda. "Such rumours have no grounds," he said.

He also said he did not want to run TNK-BP after Russian media reported Russian shareholders had asked BP to replace Dudley with Vekselberg. (Reporting by Ekaterina Golubkova, Melissa Akin, Guy Faulconbridge, Polina Devitt, Robin Paxton; Additional reporting by Tom Bergin in London; Writing by Tanya Mosolova; Editing by Quentin Bryar/Rory Channing)