Tens of thousands of Russians prepared Friday to hold their biggest protest yet over a contested election that has sent Moscow's relations with Washington spiralling to a three-year low.

Saturday's rally in Moscow -- sanctioned by the police after days of talks with the opposition -- is expected to draw around 30,000 people to a square across the river from the Kremlin following last weekend's legislative polls.

But the opposition is also organising rallies in at least 13 other major cities in a rare outpouring of mistrust in a system put in place by Prime Minister Vladimir Putin when he first became president in 2000.

Sunday's vote was narrowly won by Putin's ruling party but accompanied by a flood of video footage shot by ordinary Russians and posted on the Internet appearing to show ballot stuffing and other widespread manipulation.

The protests that followed have posed a surprise challenge to Putin and saw the Russian strongman on Thursday launch a lacerating attack on US Secretary of State Hillary Clinton for her expressions of concern.

Putin accused Clinton of deliberately sending a signal to the opposition to protest and the State Department of paying Russian groups to find fault with the elections.

He said Washington's criticism "had set the tone for some people inside the country and given a signal".

"They heard the signal and with the support of the US State Department started active work," he said in his first comments on the rallies.

US State Department spokesman Mark Toner said firmly that "nothing could be further from the truth."

Putin also vowed to toughen laws against foreign political influence while the popular Russian social networking site Vkontakte.ru revealed that the FSB security service had requested details about registered opposition groups.

The diplomatic exchange between Putin and Clinton sets a tense tone to the presidential polls next March, which are expected to see the Russian strongman return to the Kremlin for another 12 years.

Washington had attempted to "reset" ties with Putin's hand-picked successor Dmitry Medvedev after a brief 2008 war between Russia and US ally Georgia caused diplomatic tensions to rise to Soviet-era proportions.

"For the first time since the 'reset', relations between Moscow and Washington ... are starting to fray," the Vedomosti business daily remarked.

City authorities have allowed up to 30,000 people to gather on a square facing the Kremlin across the Moscow River after capping capacity to 300 at the original site requested by the opposition.

But some protest organisers have vowed to show up at the first location and then stage a march through central Moscow -- a threat that drew an immediate warning from Russia's interior minister.

"Any attempts to stage unsanctioned events and to impede order will be thwarted by interior ministry personnel in accordance with the law," said Interior Minister Rashid Nurgaliyev.

Around 1,600 people have already been arrested in three days of protests in Moscow and Putin's native city of Saint Petersburg -- a cultural capital with a tradition of opposition thought going back to pre-Soviet times.

The Kremlin faced the threat Friday of demonstrations spreading to the Russian regions after anti-Kremlin groups also organised events for cities stretching from Nizhny Novgorod on the Volga River to Krasnoyarsk in Siberia.

The Russian authorities may be "underestimating the changes occurring to the mass consciousness of society," the widely-read Kommersant broadsheet remarked.

"And it is quite possible that this may end in a catastrophe not only for the authorities but also for society."