The Biden administration warned the Russian government "that there will be consequences" if jailed Russian opposition leader Alexei Navalny dies, National Security Adviser Jake Sullivan told CNN on Sunday.

The big picture: Sullivan also defended President Biden for not mentioning Navalny in a Thursday speech about Russia or in a Tuesday call with Russian President Vladimir Putin, saying the White House aims to deal with the issue "privately and through diplomatic channels."

• Biden denounced Navalny's arrest as "totally, totally unfair" and "totally inappropriate" on Saturday, according to a pool report.

Where it stands: Navalny — Putin's fiercest and most organized domestic political critic, who previously attempted a run for president in 2018 — faces possible kidney failure as he continues his multi-week hunger strike.

• Prison authorities said they offered Navalny treatment, but he refused, arguing he should be seen by a doctor of his choice. That request was denied.
• "People usually avoid the word 'dying'. But now Alexey is dying. In his condition, it is a matter of days," tweeted the opposition leader's press secretary Kira Yarmysh on Saturday.

What he's saying: Sullivan did not specify what actions the U.S. would take against the Kremlin over Navalny's potential death, saying: "We are looking at a variety of different costs that we would impose ... but we have communicated that there will be consequences if Mr. Navalny dies."

• When asked why Biden didn't mention Navalny in his speech or a recent call with Putin, Sullivan said: "We have judged, rather than just make general statements publicly, the best way to deal with this issue is privately and through diplomatic channels direct to the upper-most levels of the Russian government."
• He also noted that the Biden administration joined the European Union in imposing sanctions "for what the Russian government has done to Navalny, for the use of a chemical weapon against him, which in contravention of international law."
• "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 international community."