Russia's Central Election Commission on Wednesday dismissed an appeal that would have allowed President Vladimir Putin to run for a third term.

The country's chief election body ruled against the appeal filed by a regional group to conduct a referendum asking citizens whether the country's president should be able to serve more than two consecutive terms, a spokesman at the commission said.

Russia's constitution bars presidents from serving more than two four-year terms in a row, but several organizations have called for an amendment that would allow the popular president to stay in power.

Putin has ruled out staying in office beyond 2008, insisting the country's constitution should be left intact.

He is believed to be choosing a successor to replace him, but some analysts have speculated that he might still choose to stay on if the Kremlin feels it is unable to guarantee his successor would be elected, and if it was made legally feasible.

A well-informed government source told CBS News' Moscow bureau Wednesday that the Kremlin supported the commission's decision to reject the referendum petition.

According to the source, who asked not to be identified because he is not authorized to speak to the media, Putin does not want to stay on for another term — at least not now.

The Wednesday ruling referred specifically to a proposal from the "Accord and Stability" group in the southern province of North Ossetia and appeared to leave the door open for other proposals on the subject.

If President Putin were to change his mind and decide to run for another term, he would have no trouble getting the Consitution and the laws amended to do so. There is one dominant political party in power, United Russia, and it has more than enough votes in the national and regional parliaments to change the Russian constitution as it sees fit. Although Putin is not a member of United Russia, the party has always backed him unconditionally.

The government source told CBS News that Putin's advisors are split on whether the president should stay on. Some of Putin's closest advisors are lobbying him to change his mind and run for a third term, because they fear losing their positions and have no obvious candidate to replace Putin.

Kremlin research shows that if a referendum were held now, a majority of the Russian people would vote to keep Putin in office for a third term, according to the CBS News source.

If the Russian people voted for Putin to stay on and he did not, the president would risk putting himself and his successor in a very uncomfortable position. He would also risk damaging Russia's delicate international image, the Kremlin source said, if the people ask him to serve a third term as president and he refuses.