Mass protests over alleged fraud in a parliamentary vote revealed the need for a major overhaul of Russia's election administration, European lawmakers said on Saturday, delivering advice Moscow is likely to see as Western meddling.

After meetings with Russian politicians and election officials, a delegation from the Parliamentary Assembly of the Council of Europe (PACE) said voters were making increasingly clear their preference for elections that are conducted fairly.

Tens of thousands of people demonstrated last month in the biggest opposition protests of Vladimir Putin's 12-year rule, alleging fraud in favour of his ruling United Russia party at the December 4 poll and calling for Russia without Putin.

Recent mass demonstrations throughout Russia ... acted as a wake-up call, the delegation led by Dutch lawmaker Tiny Kox said, according to a statement. It said fair elections should be an urgent priority for Russia.

The delegation said the low level of public confidence in the electoral system demanded a major overhaul of the election administration, and cited a pressing need for an impartial referee to oversee voting in Russia.

Putin, Russia's prime minister, is seeking to return to the presidency in a March 4 election and wants it to look cleaner than the parliamentary vote, which rival parties and international observers said was marred by evidence of ballot-box stuffing and other violations.

Web cameras are being installed at thousands of polling stations on Putin's orders, and the Kremlin has promised legislation allowing for more political parties to contest future elections.

But Putin and President Dmitry Medvedev have rejected the protest leaders' demands for a rerun of the December election, which Medvedev has said was fair, honest and democratic.

Polls show Putin is overwhelmingly favoured to win the presidency despite a decline in popularity.

He is unlikely to heed the PACE delegation's call for major changes in the electoral system or an impartial referee beyond the usual international observers.

Putin, accused by Russian and foreign critics of curtailing democracy during his 2000-2008 presidency, has often accused the West of meddling in Russian politics.

He accused the United States of stirring up protests after the December vote and said foreign countries were spending hundreds of millions of dollars to influence Russian elections.

The PACE delegation gave no specifics in its statement. PACE said the delegation was visiting Russia before the assembly's winter plenary session in Strasbourg, which is due to debate the Russian parliamentary election on Monday.

On Saturday, thousands of people demonstrated nationwide in protests organised by the Communist Party, calling for honest elections and a better standard of living.

Polls suggest Communist leader Gennady Zyuganov will come second behind Putin in the presidential election, which will go to a run-off between the top two if no candidate wins more than 50 percent of votes cast on March 4.

(Editing by Steve Gutterman)