FBK published screenshots of a decision by the Moscow prosecutor's office ordering Navalny's nationwide network to stop working while the court deliberated the extremist designations.
But the speech threatens to be overshadowed by country-wide demonstrations called by Navalny's supporters, who fear the life of Putin's best-known critic is in grave danger.
As the European Union's 27 foreign ministers held virtual talks Monday, EU foreign policy chief Josep Borrell said the bloc held the Russian authorities responsible for Navalny's health.
France's foreign minister Jean-Yves Le Drian warned Sunday those sanctions could be expanded, saying Russia must be held "responsible" for the dissident's health.
Navalny barely survived a poisoning with the Novichok nerve agent in August which he has blamed on the Kremlin. His doctors say his hunger strike might have exacerbated his condition.
Navalny, 44, a prominent opponent of Russian President Vladimir Putin, started refusing food on March 31 in protest at what he said was the refusal of prison authorities to treat him properly for acute back and leg pain.
"His condition is indeed critical," said Alexandra Zakharova, a representative of the Doctors Alliance trade union - a group that Russian authorities regard as opposition activists.
"The hostility and unpredictability of America's actions force us in general to be prepared for the worst scenarios," Kremlin spokesman Dmitry Peskov told reporters.
Moscow's ties with Washington nosedived last month when Russia recalled its ambassador after US President Joe Biden said he thought President Vladimir Putin was a killer.
The supporters had gathered outside the colony to demand access to Navalny, who is on hunger strike and demanding medical treatment for back pain and numbness in his legs and hands.
Navalny, one of President Vladimir Putin's most prominent critics, has separately complained of acute back and leg pain and accused authorities of refusing him access to his chosen doctor and of declining to supply him with the right medicine.
Navalny was arrested on his return to Russia in January, after spending months in Germany recovering from a poisoning last summer that he blames on the Kremlin.
Russia has since March impeded the speed of Twitter for not removing content it deems illegal, and threatened to block it entirely. Photos and videos take longer to load for some users.
"It was a productive discussion about how we can both work to ensure that reports of such illegal content are dealt with expeditiously," it said in a statement.
OVD-Info, which monitors the detention of political protesters and activists, published a list of more than 150 people it said had been detained.
"The police came to the forum of municipal deputies in Moscow. There are 150 people here from all over the country. Everyone is being detained. I mean, everyone," opposition politician Ilya Yashin wrote on Twitter.