A court in Moscow has granted a request to shut down another prominent human rights organisation amid a sweeping crackdown on Russian rights groups, independent media and opposition supporters.

The Moscow City Court's decision to shut down the Memorial Human Rights Centre came a day after Russia's Supreme Court revoked the legal status of its sister organisation Memorial, a human rights group that drew international acclaim for its studies of political repression in the Soviet Union.

Russian authorities previously declared both organisations as "foreign agents" - a designation that brings additional government scrutiny and carries strong pejorative connotations.

Prosecutors petitioned to shut down the groups last month, arguing they had repeatedly violated regulations obliging them to identify themselves as foreign agents in all content they produce.

"We've been saying from the start that the 'foreign agents' law - and I'm doing the air quotations again - is not lawful, and it's not to be amended but only abolished because it was designed with the aim of strangling civil society. Today, we received another proof of that," Alexander Cherkasov, board chairman of the Memorial Human Rights Centre, said.

The rulings to close them drew widespread public outrage, with crowds of supporters showing up at courthouses on Tuesday and Wednesday despite freezing weather.

Both Memorial organisations promised to appeal against the rulings revoking their legal status.

In a statement on Tuesday, Memorial vowed to "find legitimate ways to continue our work".

Several top US and European officials condemned Tuesday's decision to shut down Memorial as an attack on Russia's civil society.

Amnesty International called Wednesday's ruling to close the Memorial Human Rights Centre "yet another blow to Russia's civil society movement after years of relentless attacks".

Russian authorities have in recent months mounted pressure on rights groups, media outlets and individual journalists, naming dozens as foreign agents.

Some were declared "undesirable" - a label that outlaws organisations in Russia - or were accused of links to "undesirable" groups, and several were forced to shut down or disband themselves to prevent further prosecution.

On Saturday, the authorities blocked the website of OVD-Info - a prominent legal aid group that focuses on political arrests - and urged social media platforms to take down its accounts after a court ruled that the website contained materials that "justify actions of extremist and terrorist groups".

The group rejected the charges as politically driven.

Moscow city authorities served another prominent human rights group with an eviction notice on Tuesday.

The Civic Assistance Committee, which assists refugees and migrants in Russia, said officials handed the organisation a document voiding the agreement allowing the use of the space without compensation and ordered it to leave within a month.

"The Civic Assistance will be fighting (this)," the organisation's chair Svetlana Gannushkina said.

A number of Russian non-governmental organisations switched to operating as informal entities in recent years to avoid being affected by restrictive laws.