Navalny's lawyer Alexei Liptser said after visiting him in the hospital of penal colony No. 3 in the city of Vladimir, east of Moscow, that his health was deteriorating and he had again been denied access to his own doctors.
There was no immediate reaction from the Kremlin, but the Russian ambassador in London, Andrei Kelin, said Navalny "will not be allowed to die in prison".
Russia's prison service said Navalny, 44, was in a "satisfactory" state and he was being given "vitamin therapy" with his consent.
European Union foreign ministers are set to meet virtually Monday for talks on the health of dissident Alexei Navalny, as the United States warned Moscow of "consequences" if the Kremlin critic dies in prison and tensions soared over a Russian military build-up on Ukraine's border.
In recent years, Mr. Navalny, through brilliant combination of investigative technique, video production and social media savvy, became the leading voice criticizing Mr. Putin, documenting how the onetime KGB officer in the Kremlin became mega-rich.
Sullivan said the White House had told the Kremlin that Moscow would be "held accountable by the global community" for what happens to Navalny while in Russian custody.
Navalny is serving a three-and-a-half-year sentence over what his supporters say are trumped-up charges.
"The health of convicts in the Russia Federation can not and should not be a topic concerning them", said Putin's spokesman Dmitry Peskov.
France's Foreign Minister Jean-Yves Le Drian said Sunday that those sanctions could be expanded.
His allies have called for a nationwide rally on Wednesday, the same day that Putin is scheduled to deliver his annual state of the nation address.
Moscow has largely shrugged off global pressure since becoming a pariah to the West in 2014 when it seized Ukraine's Crimea peninsula and backed an insurgency in eastern Ukraine.
"It is the highest Russian military deployment at Ukrainian borders ever", Borrell said.
Kiev has been battling Russian-backed separatists in eastern Ukraine since 2014 and clashes intensified early this year, effectively shredding a ceasefire agreed last July.
But the arrival of a new administration in Washington in January could change the calculus if Biden presses ahead with tougher sanctions than under former President Donald Trump.
Last week, Biden signed an executive order slapping new sanctions on Russian Federation in retaliation for a major cyberbreach blamed on the Kremlin that ultimately penetrated computer systems operated by USA government agencies, including the Department of Homeland Security.
Following the U.S. sanctions, Russia recalled its ambassador to the U.S., Anatoly Antonov, and Russian Foreign Minister Sergey Lavrov publicly suggested that the U.S. should likewise recall Sullivan.
The Kremlin slammed the Czech expulsions as "provocative and unfriendly".