The statements came after Russian opposition leader Alexei Navalny was transferred to a prison hospital and the Pentagon warned about Russia's troop build-up along the border with Ukraine.
His team over the weekend said a blood test had shown showed high potassium levels and elevated creatinine, indicating Navalny could be suffering from impaired kidney function and risked cardiac arrest.
He is serving two-and-a-half years on old embezzlement charges, which he says are politically motivated, in a penal colony in the town of Pokrov around 100 kilometres (60 miles) east of Moscow.
The United States has warned Russia of unspecified "consequences" should Navalny die in Russian jail, and the White House said Monday that it is monitoring the situation closely.
"He must be treated humanely", she said.
German foreign minister Heiko Maas said the issue will be discussed at a meeting of European Union foreign ministers on Monday.
Navalny has repeatedly requested access to medical staff, but has been refused by prison authorities, prompting him to start a hunger strike three weeks ago.
Concerns over Navalny's health have mounted against the background of a spike in tensions between Moscow and the West over a litany of issues, including Russia's troop build-up on Ukraine's border, interference in U.S. elections and other perceived hostile activities.
Trump praises Putin on Fox News -- after Alexei Navalny hospitalized in prison
"The state of health of those convicted and jailed on Russian territory can not and should not be a theme of their interest", spokesperson Dmitry Peskov said.
Mr Navalny, an anti-corruption investigator, was arrested on January 17 on returning from Germany, where he spent five months recovering from a nerve-agent poisoning that he blames on the Kremlin. The penitentiary service has said Navalny was getting all the medical help he needs.
Mr. Navalny's supporters have called for a major protest across Russian Federation on Wednesday to demand his release, hours after a state-of-the-nation address by Mr. Putin. "We are talking not just about Navalny's freedom but his life", Navalny's right-hand man Leonid Volkov said on Facebook.
European leaders, including European Union foreign policy chief Josep Borrell, are assessing the bloc's strategy toward Russian Federation amid the weakening health of imprisoned opposition leader Alexei Navalny.
Russian Federation in 2020 saw record high average temperatures and a historic decline in summer ice cover on its Arctic maritime route, monitors said last month.
The prison authorities said on Monday that he has now agreed to take vitamins. His demands for a visit from an independent "civilian" physician were rebuffed by prison officials, and he began the hunger strike March 31.
In a message from prison on Friday, Navalny said prison officials threatened to force-feed him "imminently", using a "straitjacket and other pleasures".
Biden backs Japan PM on holding 'safe and secure' Olympic Games
Suga said he was grateful for the meeting and reaffirmed the "new and tight bond" between Japan and the United States. Japan is grappling with rising coronavirus infections with fewer than 100 days until the planned start.