Russian opposition deputies walked out of parliament in an unprecedented protest on Wednesday, overshadowing a speech by Vladimir Putin urging his compatriots to unite after a tense election contest.

After winning the March presidential election despite an outburst of protests against his rule, Putin outlined in a keynote address his vision for Russia's future as a top five global economy with a growing population.

But in a sign his upcoming six year Kremlin mandate may not be as unchallenged as his past 12 years in charge, an entire opposition faction walked out of the session in protest at one of Putin's comments.

Delivering possibly his last major speech as prime minister before his May 7 inauguration as Kremlin chief, Putin said the country had come through a "tense" period of "heightened emotions and political battles".

But he said it was time for all forces to work together after the turbulence of parliamentary and presidential elections that saw the opposition hold up to 100,000-strong rallies in protest at what they said were rigged polls.

"The logic of a mature democracy is that elections come to an end and afterwards a new -- and far more important period -- of joint work begins," said Putin.

"We only have one Russia, and her modern development must be the goal that unites all the political forces of the country who want to work on this aim."

But his message of unity was partially undermined by the walkout of almost the entire faction of 64 deputies from the A Just Russia party, in protest at his answer to a question about one of their members who is on hunger strike.

A Just Russia's Oleg Shein has been gone without food for 26 days along with several supporters over alleged vote rigging which he says caused his defeat in a mayoral election in the Russian Volga city of Astrakhan.

Putin said he had no authority to intervene in the case and urged the candidate to go to court. He also questioned why the hunger strike was declared before any appeal had been filed.

Faction leader Sergei Mironov, previously known as an ally of Putin, "gave the order to leave the chamber because of Putin's rudeness," A Just Russia deputy Ilya Ponomaryov tweeted.

Putin served the last four years as prime minister after emerging as Russia's undisputed number one in his 2000-2008 two terms as president, after which he temporarily handed the Kremlin to his protege Dmitry Medvedev.

He did not rule out staying in power for the maximum two consecutive terms allowed by constitution to 2024 "if the situation allows it and if I want."

However, in answer to a question, he said it would make sense to look at removing the word "consecutive" from the rule, which would make it impossible for a future president to copy his precedent of serving more than two terms.

Putin made clear that any changes to the law would have no retroactive effect. "I can tell you this sincerely as it would have no effect on me," he said.

The Russian strongman claimed that the country had emerged stronger from the perils of the 2008-2009 economic crisis and in his speech targeted a series of challenges that would build a stronger post-Soviet Russia.

Putin earmarked Russia's number one priority as reversing its post-Soviet population decline which created worries about its ability to keep sustainable populations in its far-flung Siberia and Far East regions.

"For Russia every person counts today," said Putin, warning the country would soon face the knock-on effects of the 1990s when Russia experienced its severest drop in birth rates.

The country's latest census showed that Russia's population had shrunk by 2.2 million people since 2002 and now stood at 142.9 million, but Putin in the election campaign vowed to boost the figure to 154 million.

He said economic development should turn Russia into one of the world's top five economies within the next three years but lamented that its poor investment climate risked wrecking these ambitious plans.

"If we do not improve the investment climate, we will not be able to solve a single problem standing before us in the economy, and therefore the social sphere," said Putin.