Yukos shares and the Russian stock market closed higher Tuesday, but the boosts were not enough to offset the losses of Monday's trading. Yukos gained 3.3 percent after falling 15 percent a day earlier.
Khodorkovsky was jailed Saturday on charges of tax evasion, fraud and forgery. Many perceive the four-month investigation into Yukos oil and his other companies as an attack organized by some of President Vladimir Putin's associates to avenge the tycoon's political activities, including funding of opposition parties in the run-up to the Dec. 7 parliamentary elections.
"Yesterday the situation was tense, but there is no need to panic. We have to take all measures to stabilize and restore the market," Kasyanov was quoted as saying by the Interfax news agency.
"Everyone, in his own position, should make efforts to restore the markets," he said without elaborating.
Also Tuesday, a Moscow court granted a request by prosecutors to keep a close Khodorkovsky associate, Platon Lebedev, in jail for another two months while they build their case, Interfax reported. Lebedev had been scheduled to be released Thursday but now can be held until Dec. 30.
Interfax said the request for extending his detention was based on concerns that if he was released, he could flee the country or try to pressure witnesses.
Lebedev, a top Yukos shareholder and board chairman of Menatep Group, a holding company that is a large shareholder in Yukos, was detained in July on charges of stealing state assets during the 1994 privatization of a fertilizer plant.
Khodorkovsky, whose fortune was estimated at $8 billion by Forbes magazine, is also in pretrial detention in Moscow's grim Matrosskaya Tishina jail. According to Russian law, suspects can be jailed for two months before trial but a court must approve any extension of the term.
Putin on Monday defended the prosecutors' decision to arrest Khodorkovsky, but said th're was no basis for fears that the government aimed to redistribute the state property that was privatized following the 1991 Soviet collapse.
Yukos, which this month completed arrangements to form what would be the world's fourth-largest oil company by merging with Russia's Sibneft, wields a large influence on Russian markets.