In a meeting with rights campaigners, Medvedev also said a law initiated by Putin curbing the activities of nongovernmental organizations should be changed.
Analysts warned, however, against interpreting Medvedev's statements as a rift in his ruling tandem with Putin.
According to a full transcript of the meeting published Thursday, Medvedev carefully avoided any outright criticism of Putin when responding to calls by leading rights campaigners to halt Russia's rollback of democracy.
"I would not divide relations between the state and civil society into various periods ... linked to certain people, heads of state," he said.
"There should be political competition, which cannot be substituted by anything," Medvedev added.
He told the rights campaigners, who are members of his advisory Civil Society Council, that public dialogue was essential for handling the current economic crisis.
"It is clear that in times of crisis, we should think about strengthening mutual understanding and trust between the state and the civil society," he said. "Without this, we will not be able to overcome the crisis."
Boris Makarenko, a senior analyst with Medvedev's think tank INSOR, said the president's new line was part of a coordinated policy of he and Putin rather then a sign of a rift between them. "The very choice of Medvedev as president showed that Putin was ready for a certain correction of the political style," he said. "What will happen is mild liberalization. This is a signal to elites that the ban on political competition is over.
"The crisis only made these steps more urgent," he said.
Medvedev questioned a 2005 law on NGOs that he said wrongly implied that all such organizations were enemies of the state. "There is no such aim. Real criminals who are trying to bring in dangerous developments in the life of the state never register NGOs, their activity runs in different forms," Medvedev said, suggesting that the law should be amended.
Yelena Panfilova of Transparency International Russia told Medvedev, "Administrative resources, abuse of administrative powers are increasingly substituting for real political and economic competition."
She urged Medvedev to restore the basics of democracy. "Free election, real political competition ... are the absolute instruments of civil control," she said. "Indeed, a free media is also an absolute instrument of civil control."
Lyudmila Alexeyeva, a veteran rights campaigner and a vocal Kremlin critic, said stability achieved at the expense of suppressing the opposition was elusive. "This illusion is especially dangerous now amid the crisis, when people have reasons to feel unhappy," Alexeyeva said. "Lack of opportunity to express this discontent through legal ways will build up tensions and can become a threat to stability."
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