In a statement posted on Tuesday on a pro-Khodorkovsky web site and confirmed by his lawyer Anton Drel, the former head of the oil company Yukos said the Kremlin was behind decisions by prison authorities to transfer Lebedev to the isolation cell and to move Khodorkovsky to a more crowded cell.
"On 19 August... my comrade Platon Lebedev was moved to a three-square-metre isolation cell. Platon is seriously ill," the statement said, according to Drel.
"It is obvious that they threw my friend into the isolation cell to take revenge against me, Mikhail Khodorkovsky, for my articles and interviews."
"Let the Kremlin think it is showing strength, in fact it is a display of their weakness and fear," it said, according to Drel.
Khodorkovsky, once Russia's wealthiest man, was convicted of fraud and tax evasion in May in a 13-month trial, which was widely viewed as part of a Kremlin-directed campaign to punish him for funding opposition parties and to impede his presumed personal political ambitions.
He was tried together with Lebedev, who also was sentenced to nine years.
"Let the Kremlin think it is showing strength, in fact it is a display of their weakness and fear"
In an interview published in a Russian newspaper this month, Khodorkovsky repeated his frequent contention that the prosecutor's office and trial judge were under intense political pressure, and said he believed his verdict would eventually be overturned.
Khodorkovsky has criticised the Kremlin in a range of articles and interviews, and recently said he was considering running in an upcoming by-election to the lower house of parliament, the State Duma.
Kremlin critics said his recent political statements may have prompted his move to a more crowded cell.
In his own statement issued on Tuesday, Khodorkovsky said he had begun a hunger strike - with no food or drink - to show solidarity with Lebedev.
"He knows that he is not alone," Khodorkovsky's statement said.