The UK, France, Germany, and therefore the European Union have also expressed their concern over his treatment.
Navalny’s doctors say he “will die within subsequent few days” if not given urgent medical attention for acute back pain and leg numbness.
Russia’s ambassador to the United Kingdom has said that Navalny is attention-seeking and “will not be allowed to die in prison”.
A prominent critic of President Putin, Navalny, 44, was jailed in February for old embezzlement charges, which he claims are politically motivated.
He started a fast on 31 March in protest at not having the ability to ascertain his medical team, and his doctors say recent biopsy results indicate he could suffer renal failure and enter asystole at any moment.
On Sunday, several countries joined the international protest against Navalny’s treatment inside the Russian jail within the town of Pokrov, about 100 km (62 miles) east of Moscow.
US national security adviser Jake Sullivan told CNN there would be “consequences if Mr. Navalny dies” and Russia would be “held accountable by the international community”, while President Joe Biden said his medical treatment was “totally unfair and inappropriate”.
The US is already embroiled during a diplomatic row with Russia over the near-fatal poisoning of Navalny last year, with the chemical operations agent Novichock.
The Kremlin denies Navalny’s claims that President Putin ordered the attack. But US intelligence officials concluded that the Moscow government was behind the poisoning, prompting the Biden administration to impose sanctions on senior Russian officials.
EU leaders are expected to debate things on Monday, and Josep Borrell, the bloc’s top diplomat, said the EU was “deeply concerned” and involved prison authorities to grant access to Navalny’s medical team immediately.
The UK’s ministry said during a statement: “Mr. Navalny must tend immediate access to independent medical aid. We reiterate our involve his immediate release from his politically-motivated imprisonment.”
Navalny’s 20-year-old daughter, Daria Navalnaya, who is currently studying in California, wrote “allow a doctor to ascertain my dad” on Twitter.
Navalny’s wife Yulia said he had lost 9kg (19 lbs) since starting his fast, consistent with AP.