Communist Party leader Gennady Zyuganov asked Putin to fire Kudrin over the financial crisis that has rocked investor confidence in the country and wiped hundreds of billions of dollars from Russian stock prices.
Replying to Zyuganov's speech, Putin said Russia's economic policy has "pluses, which are also the merits of the government's economic bloc".
"There are minuses too, but I will not talk about them now," he added. "We need to do everything very carefully."
Kudrin has become the darling of many bond investors since he was appointed finance minister in 2000, presiding over a spectacular turnaround of the country's public finances, helped by the oil price rise.
Kudrin, who helped land Putin his first job in Moscow in the 1990s, has earned plaudits from ratings agencies and investors for his fiscal prudence, but has caused tensions at home, where some politicians would prefer to spend Russia's oil wealth on boosting infrastructure and welfare.
The New Times magazine this week cited rumours that Putin was unhappy with Kudrin's opposition to the government's market rescue plan and wanted to replace him, but a source at the Finance Ministry denied there was a rift between the two men.
On Thursday, Putin echoed Kudrin's fiscal prudence.
"We should not constantly increase social obligations without thinking about the consequences for the budget. ?€¦ Will it be able to provide for such a level of obligations?," he said.
Much of the $210 billion market rescue package unveiled by the authorities over the past month will have to be paid for by money from the budget.
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