Communist Party leader Gennady Zyuganov and Liberal Democratic Party head Vladimir Zhirinovsky suggested last month that Putin would step down next year to prevent the worsening economy from damaging his personal popularity.
"It has always been a rule for me never to run away from problems," Putin said as he fielded questions from reporters after his televised question-and-answer show. "You have to fight these problems and take full responsibility for what you do."
In answer to a question from a BBC reporter, he also ruled out presidential election before 2012, when President Dmitry Medvedev's current term ends.
Putin didn't need a translator to understand the sense of the question, asked in English, of whether he could "categorically" rule out a return to the Kremlin next year.
"I want to tell you that President Medvedev and I have worked out a very effective tandem," he said. "I, for example, very much like the nature of our cooperation."
Putin went as far as to say he wasn't sure about a possible return to the Kremlin within the next 12 months.
"The next elections in the Russian Federation are in 2012, and I think everyone must do his duty in his current position, and there's no need for fidgeting over what will happen in 2012," he said. "If we live till then, we'll see."
Zyuganov said last month that Putin intended to step down as prime minister after the constitutional amendments to extend presidential and State Duma terms take effect next year.
He didn't elaborate on what he thought Putin would do after, but a number of analysts have suggested that Putin was aiming for a return to the presidency.
Zyuganov made the statement after Medvedev, in his Nov. 5 state-of-the-nation address, proposed extending Duma terms to five years from four and presidential terms to six years from four.
The Kremlin quickly sent the proposals to the Duma, which approved them in less than a week.
They are now garnering the approvals from regional legislatures necessary before Medvedev signs them into law.
Putin said he was content with the performance of his ministers and was not planning any firings over the handling of the economic crisis.
"Some measures could have been taken more promptly," he said, without providing any examples. "But on the whole, the measures we are taking are adequate."
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