A Russian court on Tuesday imposed sweeping bans on Alexei Navalny's Anti-Corruption Foundation (FBK), its director said, as Russia inches toward shutting down the jailed opposition figure's movement. 

Foundation director Ivan Zhdanov said on Twitter the court had banned the FBK from posting content on the internet, using state media, organising protests, participating in elections and using bank deposits.

The bans came as the court considers whether to designate the FBK and Navalny's national network of regional offices as extremist organisations, putting them on par with the Islamic State group and Al-Qaeda and banning them in Russia.

Earlier Tuesday the Moscow city court's press service told reporters a judge had agreed to a "ban on certain activities" for the FBK without clarifying what they were as the case is being heard behind closed doors.

European Union foreign affairs chief Josep Borrell warned Moscow the moves were against international obligations.

"Suspending all activities of organisations affiliated with Alexei @navalny incl his Anti-Corruption Foundation runs counter to Russia’s international obligations," he tweeted.

"I urge Russian authorities to reconsider recent decisions & to end their systematic crackdown on fundamental rights," Borrell said.

The bans follow a ruling on Monday ordering Navalny's regional offices to stop working while the court decided on the request for the designation.

Navalny's team took a dim view with the FBK calling the move a "huge blow" and the offices said they would stop operations immediately to protect their employees and supporters. 

They promised however to continue fighting corruption, the ruling United Russia party and President Vladimir Putin "in a personal capacity".

The team adopted a fighting stance Tuesday.

Zhdanov said that the bans would not affect the FBK's work, while the group tweeted that it had heard it was "banned again". 

"Yesterday they banned us and they will completely ban us again the day after tomorrow," the FBK said.

"Therefore we have important information for you to keep in mind at this time," the group added. 

"Putin is a thief and a murderer. United Russia is a party of crooks and thieves."

Increasing pressure

Prosecutors this month said they requested the extremism label for Navalny's groups because they were destabilising the country and working to alter "the foundations of the constitutional order". 

If designated as extremist, members of the groups could face lengthy prison sentences if they continue working.  

Russian riot police officers block a street during a pro-Navalny rally in Moscow. Photo: AFP

Navalny, Putin's best known domestic critic, launched the FBK in 2011.

The group has since routinely released investigations into alleged graft by officials at all levels of government, often accompanied by YouTube videos.

Navalny's regional offices support his graft investigations as well as his Smart Voting strategy, which directs voters to cast their ballots for candidates best placed to defeat Kremlin-linked opponents. 

The 44-year-old opposition figure was arrested in January after returning to Russia from Germany, where he had spent months recovering from a poisoning attack he blames on Putin. 

He is serving two-and-a-half years in a penal colony outside of Moscow for violating parole terms on old fraud charges he and his allies say are politically motivated. 

The opposition figure says he has been denied adequate medical treatment for severe back pain and numbness in his limbs in prison. Last week he ended a 24-day hunger strike after he was examined at a civilian hospital.

He has also complained of "torture" through sleep deprivation, saying he is woken up every hour all night because he is considered a flight risk by the authorities.

His defence team has filed a lawsuit against the penal colony over the classification, and on Tuesday a Moscow court told the Interfax news agency that the team has also sued a detention centre in the Russian capital where he was first held after his arrest.

Authorities have ratcheted up pressure against Navalny's allies since his return to Russia, with many top aides having left the country or been placed under house arrest.