"Losses to the state budget total over 22.5 billion rubles ($879.6 million)," the statement read.
In May a law enforcement source said Semyon Kukes, former head of the Tyumen Oil Company (TNK), was suspected of gross tax evasion.
Investigators are also looking into tax evasion charges against former executives of Slavneft.
Slavneft, one of Russia's top 10 crude producers, is co-owned by Gazprom Neft, the oil arm of Russian energy giant Gazprom, and Russian-British joint oil venture TNK-BP.
Maj. Gen. Alexander Matveyev, deputy head of the Investigations Committee, said that both companies had already paid damages to the state.
The British oil giant and the Alfa Access-Renova consortium of Russian billionaire shareholders signed last week a memorandum of understanding that should put an end to their protracted dispute over the joint oil venture's management. It includes an option to sell up to 20% of a TNK-BP subsidiary through an IPO on international financial markets.
The deal is a concession by BP to a number of its Russian partners' demands, including the removal of BP-appointed chief executive Robert Dudley, whom they accused of acting only in BP's interests, and the appointment of three independent executives.
The British oil major earlier accused the Russian shareholders of orchestrating a state harassment campaign against TNK-BP, Russia's third largest producer, and seeking to seize control of the venture.
