A RUSSIAN court has slapped $US13,000 ($A12,720) worth of fines on the election monitor Golos, in the first ruling under a new "foreign agent" law that observers say will lead to closures of many organisations across the country.

The move on Thursday comes amid mounting criticism from activists that Moscow is cracking down on NGOs with repressive laws and a wave of raids on their offices by prosecutors.

Golos (Voice), a group that monitors Russian elections for violations, and its director Liliya Shibanova, were ordered to pay the fine by Moscow's Presnensky district court for failing to register as a "foreign agent" as required by new legislation.

The organisation denied the label applied to them and said it would appeal the ruling.

The Russian parliament last year passed a law obliging all NGOs who receive money from abroad and engage in political activity to register as foreign agents, in a move activists slammed as a throwback to Soviet times.

During his annual televised question-and-answer session on Thursday, President Vladimir Putin denied he was persecuting NGOs.

"Let them say where they got the money, how much money, and how they spent it! What's wrong with that? In the United States such law has been working since 1938," he said.

The US ambassador to Russia Michael McFaul swiftly reacted to the rulings, writing on Twitter that he is "disappointed in the decision", while Human Rights Watch and Amnesty International called it "an alarming indicator for the future of civil society in Russia" in a joint statement.

Patrick Ventrell, deputy spokesman of the US State Department, said: "We're very concerned that the election monitoring NGO Golos has been declared a foreign agent and fined thousands of dollars - the first conviction under Russia's 2012 law on NGOs."

The court based its ruling against Golos on information that it had received money as part of a human rights prize from Norway.

But the group tried to prove in court that they refused to take the money, part of the Andrei Sakharov Freedom prize.

"Golos told the Norway Helsinki Committee that it was unable to receive the monetary award precisely because of the 'foreign agent' law," said Ramil Akhmetgaliyev, a lawyer who represented the group in court.

The money was returned, and the Norwegian group apologised for their mistake, he added in a statement sent out by the Agora association of lawyers.

But the judge ruled that Golos was acting as a "foreign agent" without declaring itself as such, and sentenced it to a fine of 300,000 roubles (about $A9785).

The group's director Shibanova was also fined 100,000 roubles in a separate hearing.

Other Russian NGOs who have watched the case against Golos are now expecting a similar wave of hearings.