"We have communicated to the Russian government that what happens to Mr Navalny in their custody is their responsibility and they will be held accountable by the global community", national security adviser Jake Sullivan told USA media.
A medical trade union with ties to Navalny said on Saturday he was in critical condition, citing medical tests that it said showed that Navalny's kidneys could soon fail, which could lead to cardiac arrest.
Authorities have ramped up pressure on Navalny's supporters in recent months, detaining more than 10,000 protesters at opposition demonstrations in January and February. "An extreme situation demands extreme decisions".
German foreign minister Heiko Maas said the issue will be discussed at a meeting of European Union foreign ministers on Monday.
French Foreign Minister Jean-Yves Le Drian has said his country is "extremely concerned" about the health of Alexei Navalny, the outspoken critic of Russian President Vladimir Putin, who is on a hunger strike in a penal colony.More news: Czech police hunt two men wanted over Salisbury novichok poisonings
Volkov said Wednesday's rally - set for 7 p.m. local time - could become a decisive battle against "absolute evil" or Russia's last opposition rally for years to come. They have pledged to ensure he survives.
In a message calling for the protests, his team said Navalny's life is now "hanging by a hair" and accused the Kremlin of "killing Navalny for a second time before the eyes of all Russian Federation". We call on the Russian authorities to grant him immediate access to medical professionals he trusts.
Navalny, Putin's most prominent opponent, was arrested in January on returning to Russian Federation after recovering from a near-fatal poisoning attack he says was orchestrated by the Kremlin.
Russian Federation jailed Mr Navalny for two-and-a-half years in for parole violations he says are fabricated.
The Kremlin has denied any involvement but also refused to investigate the incident - maintaining there is no definitive proof Navalny was ever poisoned.More news: Iran offers upbeat assessment of progress in nuclear talks
Mr Navalny's supporters face the prospect of their movement being officially outlawed and declared extremist.
Navalny began refusing food on March 31 in protest at what he said was the refusal of prison authorities to provide him with adequate medical care for acute back and leg pain.
The same day, a group of celebrities penned an open letter calling on Putin to allow Navalny to receive medical treatment from a doctor of his choice.
On Sunday, a number of countries joined the worldwide protest against Mr Navalny's treatment.
"Navalny is now in a prison camp and his life is hanging by a thread".More news: Indiana Fedex shooting massacre: Names of victims revealed
Last week, Russian Foreign Ministry's spokeswoman, Maria Zakharova, said that the United States is making up "stories" about Navalny's detention conditions while the USA itself continues to violate the rights of prisoners.