It asked the court to find the two men guilty of stealing 218 million tons of oil from a daughter company of Yukos between 1998 and 2003.
Last week the court said it had enough evidence to prove Khodorkovsky's and Lebedev's guilt.
The two oligarchs are already serving eight-year sentences for fraud and tax evasion. In May, they were accused of stealing $9.6 billion from the $15.8 billion profit generated by Yukos between 1999 and 2003, as well as 350 million tons of oil.
The prosecutor cited arithmetic errors and a lack of evidence for the new turn of affairs.
On Friday the prosecution had already dropped the volume of stolen oil by 20 million tons.
Once Russia's richest man, Khodorkovsky claims the charges against him are politically motivated.
