Russian Federation jailed Mr Navalny for two-and-a-half years in for parole violations he says are fabricated.
A day after Navalny's doctors said Vladimir Putin's most prominent critic could die "any minute", US President Joe Biden's national security adviser said Washington had warned the Kremlin that it would be "held accountable by the global community" if he died.
On Sunday, France, Germany and the European Union (EU) joined growing chorus over Navalny's plight.
European Commission President Ursula von der Leyen and German Foreign Minister Heiko Maas called for Navalny to receive immediate medical care as did the US State Department, while French President Emmanuel Macron said world powers should draw "clear red lines" with Russian Federation and consider possible sanctions when they are crossed.
Supporters of Alexei Navalny stage a demonstration outside Downing Street in London, Britain, on 13 April, 2021.
Sullivan added that Kremlin was told "that there will be consequences if Mr Navalny dies".
Biden was asked to comment on Navalny's detention conditions on Saturday.
Navalny's team said said next week's protests have become a final showdown with the Kremlin to stop Navalny's death and prevent the complete destruction of a democratic opposition in Russian Federation.
Volkov said Wednesday's rally could become a decisive battle against "absolute evil" or Russia's last opposition rally for years to come.
Prison authorities say they have offered Navalny proper medical care, but that he has refused the treatment in favor of being treated by a doctor of his choice from outside the facility, a request that authorities have declined.
Navalny has said prison authorities are threatening to put him in a straitjacket to force-feed him unless he accepts food.
Some activists have called for him to be flown out of the country for emergency medical care.
In January, the Kremlin was able to shut down protests that broke out after Navalny returned to Russian Federation and was jailed on parole violations that have been widely condemned as politically motivated.
"Our patient could die at any moment", he said in a Facebook post.
The authorities cast Mr Navalny and his supporters as US-backed subversives bent on destabilising Russian Federation and moves are underway to declare them extremists, opening the door to long jail terms.
He went on hunger strike to protest the refusal to let them visit when he began experiencing severe back pain and a loss of feeling in his legs.
One of the doctors, Yaroslav Ashikhmin, said the tests also suggested that Navalny's kidneys are now shutting down.
More than 70 prominent actors, writers, artists and academics, including Jude Law, Vanessa Redgrave and Benedict Cumberbatch, have called on Putin to ensure that Navalny receives proper treatment immediately.