Khodorkovskii's lawyer, Anton Drel, said an offer from Khodorkovskii to turn over 44 percent of the shares in Yukos to settle the tax claim is still on the table.
Judges in the trial rejected a plea from Lebedev to be released on grounds of ill health.
The trial was adjourned and is scheduled to resume on 13 July.
Meanwhile, Yukos' new chief executive, Stephen Theede, today reportedly offered the government $7.5 billion over a three-year period to cover tax arrears.
Russian tax authorities say Yukos owes nearly $7 billion in back taxes for 2000 and 2001.
Officials are said to be considering the offer.