The first auction, set for February 14 and then moved to March 14, was called off since there were no takers, apparently because of the excessive price.
The starting price was set at 2,885,500,000 rubles (about $108.9 million). Each bidder had to place a deposit of 450 million rubles (about $16.9 million).
"A relevant resolution will be signed in the near future," a ministry spokesman said.
The government's S7 stake was included in the 2006 privatization plan.
S7, Russia's second-largest air carrier after Aeroflot, changed its name from Sibir in March 2006.
The airline was dogged by a series of misfortunes last year, including an air disaster in the Siberian city of Irkutsk July 9, when an Airbus 310 crashed on landing, killing at least 124 and injuring 70.
