Officials had earlier said they expected to get $2.7 billion, but shares in companies which constitute Svyazinvest have risen sharply this year on expectations of the holding firm's privatisation.
"I think we should get at least $3.3 billion," the agency's head Valery Nazarov told reporters. He said he backs an auction for the stake of 75 percent less one share, not an initial public offering.
Nazarov, however, said there had been no official evaluation of the stake.
The market is still waiting for a presidential decree to privatise Svyazinvest, which could become Russia's biggest privatisation to date. But wrangling inside the government has slowed the deal this year.
President Vladimir Putin must sign a decree to privatise Svyazinvest because the holding, which unites seven regional telecoms firms, long-distance monopoly Rostelekom and Moscow's fixed-line monopoly MGTS, services the government and the military.
Economy Minister German Gref said in November the sale of Svyazinvest could take place in the second half of 2006.
But the government is yet undecided on how the holding should be sold.
Earlier this month the head of Russia's financial markets regulator advocated a sale via financial markets, but on Wednesday Nazarov backed an auction. "I know potential buyers," he said. "There are around three of them."
One of Russia's biggest conglomerates, Alfa Group, has said it would like to participate in an auction. One of the country's biggest consumer holdings, Sistema, raised $1.56 billion in an initial public offering in London to finance an acquisition of Svyazinvest. Telecoms firm Telekominvest has also expressed interest in the sale.
Russia sold 25 percent plus one share of Svyazinvest in 1997 to international financier George Soros for $1.87 billion.
Soros later called it his worst-ever investment and has sold it for $625 million to a US businessman of Russian origin, Len Blavatnik, who has said he will also participate in the sale.