Sources close to both the bank and the oil major, however, said a stake of less than 5 percent had been acquired.
The government has been snapping up significant assets and equity stakes in recent months as the recession lowers company valuations, capitalizing on the downturn to gain greater control of strategic industries.
LUKoil, in which ConocoPhillips holds a 20 percent stake, is seen as one of the last bastions of private ownership in an industry heavily dominated by the state. About 28 percent of its shares are publicly traded.
Spokespeople for both LUKoil and VEB declined to elaborate on the deal.
"The company welcomes VEB, one of the largest state financial institutions in Russia and a strategic investor in the real economy, as one of its investors," LUKoil vice president Leonid Fedun said in a statement.
Norilsk Nickel announced last week that VEB had acquired 3.7 percent of its shares through the support program.
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