Mikhail S. Gutseriev, who was once in the tight coterie of Russian billionaires known as oligarchs but has since fallen from favor, accused the government of President Vladimir V. Putin of forcing him out of the company using trumped-up tax claims. The critical letter was the first significant public challenge to Mr. Putin from an influential businessman since the imprisonment four years ago of Mikhail B. Khodorkovsky, the former chairman of Yukos Oil, who is serving an eight-year sentence in Siberia. The development left analysts wondering what the future holds now for Mr. Gutseriev.