The head of the Russian oil giant Yukos stepped down, eight days after he was arrested for fraud and tax evasion.

In a statement released through his lawyers, Khodorkovsky said: "As a manager I should do everything to deflect from the workforce the blows aimed at my partners and myself. I am leaving the company. I am confident that the highly professional, united team of extremely experienced managers will be able to successfully handle the task of globalising the Yukos / Sibneft business."

Yukos shares have begun to recover this week, yet a lengthy criminal prosecution could only spell turmoil for its share value. Yukos shares leapt 4.1% on the news.

When Khodorkovsky was locked up October 25, the Russian stock market plunged due to concerns about the country's economic recovery. Russia's economy had grown for the past four years, and its stock market was thriving before it suffered a series of shocks during the 4-month-old probe against Yukos.

The resignation came as Russian prosecutors said they were to investigate the 1995 privatisation of Sibneft, the oil company that made Chelsea soccer boss Roman Abramovich much of his fortune.

The investigation has been prompted by a complaint from the same MP who started the Yukos affair, adding to fears that the Kremlin pursuit of big business might spread.

In the complaint Yudin accuses Abramovich of widespread irregularities amid the 1995 selloff of Sibneft's assets for $US137m. The complaint eerily resembles the start of the investigation against Yukos associates in July.