That seemed to mark a turnaround for the staunch fiscal hawk, who on Tuesday said he saw no scope for tax cuts and that if any energy producers were unhappy with this, there would be plenty of others willing to take over their deposits.
Instead, he proposed tax hikes to help shore up the pension system.
The issue is a thorny one in Russia, where businesses and the growth-focused Economic Development Ministry have countered the Finance Ministry's tax-hike plans with proposals for cuts.
"If we don't cut value-added tax and others, then we'll take another look at the oil taxes," Kudrin said. "It's possible. We will consider it. But I am not willing to give a time frame."
His comments appeared to chime with calls for a compromise on the issue from Kremlin economic aide Arkady Dvorkovich on Tuesday.
President Dmitry Medvedev is expected to make the final decision on tax reform later this month.
There were signs that the business lobby, which had earlier described the Finance Ministry's long-term budget strategy as "unacceptable," could be ready for the compromise.
"This is a sensible approach," Alexander Shokhin, the head of the Russian Union of Industrialists and Entrepreneurs, told reporters after Kudrin's latest remarks.
Another potential sticking point remains VAT, which the Economic Development Ministry wants to cut to 12 to 13 percent, from 18 percent currently.
Kudrin estimated that cutting VAT and offsetting that with energy revenue would drive inflation higher by 3.8 percentage points.
"It's like fighting a fire with kerosene, from the standpoint of financial stability," he said, adding that it would reduce the private savings rate and boost Russia's fiscal dependence on oil.
Inflation is a big problem in Russia, with consumer prices already up 9.8 percent since the start of 2008.
Taxes are also an important issue for Russian companies, and Kudrin's comments against any more cuts for the energy sector helped send the country's stock market to fresh two-year lows.
Oil companies pay a progressive tax on the oil they sell, limiting their upside from high prices. Suggestions of changes to the oil-tax regime tend to drive swings in stock prices.
"With oil prices going down, the government may simply be unable to find room for further tax cuts in its 2010 budget plan," analysts at VTB Capital said in a research note.
"Should the government decide to freeze the tax reforms that had earlier been hinted at by the Energy Ministry and oil majors, the oil sector could lose an important medium-term value trigger."
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