US oil and gas giant ExxonMobil is demanding millions of euros in back taxes from Russia.
Russian officials say Exxon chief executive Rex Tillerson was in Moscow for closed-door meetings with Energy Minister Alexander Novak.
The Kommersant daily says Tillerson is contesting taxes paid on the Sakhalin-1 project in the Far East operated by ExxonMobil.
Exxon, which owns 30 percent of the operation, claims it overpaid on the project.
The company has allegedly been paying 35 percent of its profit to Moscow despite the state reducing taxes to 20 percent in 2009.
Kommersant said while Exxon had not insisted on the issue in the past years, Western sanctions over Russia had prompted the company to change tack.
The company is reportedly threatening to file a complaint against Moscow at the international court of arbitration in Stockholm.
Sources quoted by the daily said the amount involved was up to 150 million euros ($160 million).
ExxonMobil has nurtured close ties with Rosneft in recent years, launching numerous joint projects in the Arctic and Far East.
The Russian oil giant however has been hit by Western sanctions resulting in several projects being frozen.
In February, ExxonMobil said it had racked up a billion dollars in loss of potential earnings as a result.
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