Pornography website PornHub has uploaded an anti-corruption documentary critical of Russian officials after it was banned by a Moscow court.

The adult video-streaming website reached out to blogger Alexey Navalny shortly after he was ordered to remove his video on Wednesday.

The video retitled by the adult website "Russian Corrupted Politician F---ed Hard", alleges large-scale corruption by Russian Prime Minister Dmitry Medvedev and accuses him of amassing a shadowy property empire.

It was viewed more than 21 million times on YouTube before a Moscow court ordered Navalny take it down after Kremlin-connected billionaire Alisher Usmanov challenged accusations he had given a mansion as a bribe.

Kremlin critic Alexei Navalny, who was arrested during a March 26 anti-corruption rally. (AFP)

"We didn't doubt there would be such a decision," Navalny told journalists outside the court, insisting he would not take the video down.

"The investigation is based on facts," he added.

PornHub reached out to Navalny on Russian social media site VKontakte and invited him to publish more anti-Russian government films on its homepage.

"Thank you, I will not be deleting it anyway," he wrote back to PornHub, NewsWeek reports.

He also suggested PornHub should remake its own version of his documentary in its adult "relevant genre".

Russian Prime Minister Dmitry Medvedev has been accused of corruption in Navalny's banned documentary. (AFP)

Usmanov has accumulated a fortune of $20.5 billion from metallurgy and interests in social media, according to Forbes magazine's rich list, and owns 30 percent of London football club Arsenal.

His lawyer Genrikh Padva said after the Moscow court decision that he was "very glad we managed to defend someone's good name," news agency RIA Novosti reported.

The Russian interior ministry said that it had looked into the claims made by Navalny and found no crime.

Navalny, a lawyer turned blogger, came to fame at the head of anti-Putin rallies in the winter of 2011 and 2012. His team works on exposing the lavish lifestyles of the Kremlin elite.

The blogger's anti-government actions have garnered both acclaim and criticism. In March he was attacked with green food dye after using an ATM.

Navalny posted a blog "I Will Not Delete It" after yesterday's ruling warning that he would not comply with the court’s decision.

The lawyer has announced he will run in next year's Russian presidential election - which Putin is widely expected to compete in.