The joint venture has been increasingly troubled in recent months
BP has said the chief executive of its Russian joint venture TNK-BP has temporarily left Russia because of "sustained harassment".
Robert Dudley will run the company from outside the country and BP said that TNK-BP would operate as normal.
This year TNK-BP has faced lawsuits, visa rows and industrial spying claims, as well as arguments over investment and the future role of Mr Dudley.
The Russian shareholders said the claims of harassment were "insulting".
They reiterated their call for a new chief executive.
Mr Dudley said he had decided to leave because of uncertainty surrounding his work visa and the "sustained harassment" of the company and himself.
He said that despite having a valid employment contract, he had been unable to obtain a work visa and a transit visa was due to expire on Sunday.
"In addition..., the company and I have faced unprecedented investigations, proceedings, enquiries and other burdens," he said in a statement.
Mr Dudley's visa has not been renewed on the grounds that he allegedly does not have a valid work contract.
He hoped his decision would mean the "administrative pressure" on the company would now ease.
BP owns 50% of the venture while the Russian shareholding is made up of a number of Russian billionaires who control a consortium known as Alfa Access Renova (AAR).
On Thursday, AAR said that Mr Dudley's employment contract had run out in December and said that AAR had not interfered with the decisions of the Russian authorities on his work visa.
Mr Dudley said the dispute had created unstable working conditions
It said the allegations of harassment were "deeply inappropriate and insulting".
Mikhail Fridman, one of the billionaire investors and TNK-BP's chairman, said that it was a "ridiculous notion that the company could be run by remote control from London".
"TNK-BP is an independent oil company in which BP is not a controlling shareholder," Mr Fridman said.
"We continue to insist that BP nominate a new independent chief executive office who would be based in Moscow and manage TNK-BP in the interest of all shareholders."
The Russian investors have accused Mr Dudley of acting only in BP's interests.
AAR is also said to want higher dividend payments from the venture.
BP executives expressed their outrage at what they called "an orchestrated campaign of harassment" in the increasingly bitter dispute.
On Tuesday, BP said it had pulled out its last 60 technical specialists from Russia, following 90 who had already left.
Peter Sutherland, chairman of BP, said that AAR's actions were doing "enormous damage" to Russia's reputation as a place to do business.
"It saddens me that nowhere in our recent history have we been treated as we are currently being treated in Russia," he said.
"There has even been manipulation of elements of the Russian state as part of this campaign."
Lord George Robertson, deputy chairman of TNK-BP, said that the behaviour of AAR was outrageous.
"AAR's efforts to wrest control of the company through illegitimate means are damaging the company and, regrettably, Russia's reputation among international investors," he said.