Dudley made the statement on the sidelines of an international economic forum in St. Petersburg.
In late May, Russia's consortium AlfaAccessRenova (AAR), a co-owner of TNK-BP, demanded that Dudley step down, accusing him of putting the interests of BP first. On May 30 British shareholders at TNK-BP reiterated their trust in and backing for Dudley.
According to previous AAR statements, its disagreement with BP concerns TNK-BP's development strategy, primarily international expansion.
TNK-BP's executive director Viktor Vekselberg earlier said that he expected TNK-BP shareholders to reach a preliminary agreement and move closer to resolving the conflict in the next few days.
On Friday Russian Deputy Prime Minister Igor Sechin said at a meeting with BP CEO Tony Hayward that Moscow would not get involved in the conflict.
Founded in 2003, the Russian-British venture TNK-BP, Russia's third-largest oil producer, is jointly owned by BP and AAR. The consortium representing the Russian investors - the Alfa Group, Access Industries and Renova (AAR) - holds 50% in the energy company. Dudley was appointed president and CEO in 2003, when the joint venture was set up.