Russian President Vladimir Putin on Monday used a traditional New Year address to call for unity following a year of protests against his return to the Kremlin for a third term.

The country's "development and fate depend on our enthusiasm and labour, on our unity and responsibility," ITAR-TASS news agency quoted Putin as saying in the televised message aired first in Russia's Far East.

"Only together can we, the people of Russia, advance steadily, cope with any trials, solve the most complicated tasks, build a strong, successful state, a modern, prosperous and free society," said Putin.

Russia was rocked by its largest post-Soviet protests in response to Putin's decision to seek the presidency again following a 2000-2008 spell in power in which the state cracked down on civil liberties and media rights.

The former KGB spy served as prime minister for four years under his hand-picked presidential successor Dmitry Medvedev before announcing in September 2011 that the two had agreed to a job swap.

Putin then won March elections and was sworn in as president in May.

His inauguration was preceded by violent protests outside the Kremlin and was followed by the adoption of laws further restricting Russians's right to join demonstrations not authorised by the state.

The strength of such rallies has tapered off in recent months as the opposition scrambles for a strategy that could work with Putin firmly cemented in power at least through 2018.

But smaller-scale rallies still periodically continue in Moscow and Saint Petersburg -- Russia's tsarist capital and the home town of both Putin and many of his closest ministers and advisers.

The radical wing of Russia's opposition movement vowed to hold a traditional New Year's Eve rally in central Moscow later Monday despite failing to win permission for the event from the city.