Medvedev has promised to continue the policies of his mentor, outgoing President Vladimir Putin. But some observers have predicted the next president may adopt a more consensual style.
"Our task is to create a system that would allow civic structures to participate in working out state policy and appraising its quality," Medvedev told members of the Public Chamber.
Putin's rule has brought growing restrictions on nongovernmental organizations, especially those focusing on human rights and funded from abroad.
Medvedev said the opinion of minority groups represented by public organizations and professional unions should be taken into account.
"The voice of such groups should be heard in our society," Medvedev said. "There should be a practical mechanism for defending their rights and interests. Only in this way can our society become truly harmonious."
Medvedev told the Public Chamber he wanted civil society groups to scrutinize legislation before it came into force.
Medvedev, a 42-year-old former lawyer elected on March 2, said a mature civic society was essential if Russia was to achieve the target set by Putin of modernizing its economy.
"Our actions should be focused on switching the economy and social life to a new, innovative mode," he said.
Some Kremlin-watchers predict that Medvedev's policies will be more liberal and market-oriented than under Putin.
Skeptics point out that Putin will remain a strong influence and that Medvedev, as chairman of Gazprom, has played a key role in returning private energy assets to Kremlin control.
Gazprom has also acquired control over NTV, once the country's biggest private television station, and the head of a subsidiary has bought the newspaper Kommersant, fueling accusations that free speech in Russia is under threat.
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