Russian scientists staged a rare anti-government demonstration Saturday, amid fears that after cracking down on the media, rights activists and the opposition, the Kremlin is now training its sights on science.

Several thousand protesters including scientists and intellectuals took to the streets of Moscow to express fears that scientific research in Russia faces dire prospects due to stifling bureaucracy and mismanagement.

Prominent opposition figures including top activist Alexei Navalny joined the rally.

"Authorities are strangling science" and "Nobel laureates are foreign agents" read some of the placards held by protesters.

"Putin cannot solve problems, he is the problem," read another sign.

Astrophysicist Boris Shtern told the rally: "Alas, science is slowly dying. The massive advance of ignorance is being supported by the media and authorities."

The protest was originally called in support of a top private foundation whose 82-year-old founder, philanthropist Dmitry Zimin, has recently come under fire for financing Russian science from overseas accounts.

Discontent among scientists has been brewing for months but the crackdown against Zimin's Dynasty Foundation sparked acute anger and disbelief.

The justice ministry in late May added the Dynasty foundation, set up by ex-telecoms magnate Zimin, to its list of "foreign agents" under a law that critics say is designed to muzzle critics of President Vladimir Putin.

Zimin, a hugely-respected former radio engineer who spent millions of dollars supporting Russian scientific research, has threatened to shut down his foundation, demanded an apology from the authorities and temporarily left Russia.

An AFP correspondent said more than 2,000 people turned out for the rally, while activists counted some 3,500 participants.

Antonina Aleksandrova, a biologist at a cancer treatment centre in Moscow, slammed the attack against Zimin's foundation.

"For the country to develop, it needs education," Aleksandrova told AFP.

"The Dynasty is an egregious example of how an organisation that played a huge role in this education has been crushed."

"It is a significant loss for us all."

Physicist Vladimir Olshansky said he found the current atmosphere of "lies and obscurantism" offensive.

He said the Kremlin was threatened by free-wheeling scientists and their independent-minded benefactors.

"The authorities believe that they themselves know who to give money.

"What's happening threatens the country more than science," added chemist Efim Brodsky.

Putin signed the law on "foreign agents" in 2012, after huge opposition protests rattled Russia at the time, and described the legislation as "self-defence" against the financing of political activities in the country from abroad.

The law has already hit scores of rights groups which resent the tag carrying connotations of Cold War espionage.

The Dynasty foundation will convene a meeting on Monday to decide its future strategy.