Russian President Vladimir Putin on Monday dismissed claims by opposition leader Alexei Navalny that he owns a luxury property on the Black Sea worth $1.35 billion, as the opposition urged fresh nationwide demonstrations.

Courts around Russia started handing down short jail sentences to demonstrators arrested during nationwide opposition rallies last weekend, while the foreign ministry accused US diplomats of encouraging Russians to join the protests.

Navalny's aides urged his supporters to take to the streets again next Sunday ahead of a court case that could see Russia's most prominent Kremlin critic put behind bars for more than three years.

The 44-year-old campaigner was detained just over a week ago when he returned to Moscow from Germany, where he had been recuperating from exposure to a Soviet-designed toxin.

He called on his supporters in dozens of cities to rally last weekend and released a two-hour investigation into the palatial seaside property to spur allies to demonstrate.

The rallies saw a record number of arrests, and Putin on Monday denied having anything to do with the property in Navalny's video, which has now been watched 86 million times.

"Nothing that is listed there as my property belongs to me or my close relatives, and never did," Putin said during a video call with Russian students.

Navalny's report -- his most-watched anti-corruption probe by far -- claims the property is worth $1.35 billion and features everything from an underground ice rink to a casino.

Leonid Volkov, a key aide to the Kremlin critic, urged Russians to take to the streets again on January 31 "for Navalny's freedom, for freedom for all, and for justice".

Saturday's rallies saw clashes between police and protesters, 3,700 of whom were detained according to the OVD-Info monitoring group.

Putin said on Monday that Russian citizens have the right to express themselves but that they must do so "within the framework of the law".

According to OVD-Info, by Monday morning more than 80 people have been handed short-term jail sentences over the protests while at least 15 criminal probes have been launched.

Putin also said minors should not be encouraged to join the rallies, referring to a claim repeated by authorities that the opposition had encouraged young people to protest.