MOSCOW — A leader of the Russian opposition who has been a vocal critic of what he calls a Kremlin policy of assassinating political enemies has fallen into a life-threatening coma caused by an unknown poison, his wife said on Monday.

The diagnosis of what ailed Vladimir Kara-Murza came at a delicate political moment for the United States and Russia, as President Trump had just brushed aside criticism of the Russian president, Vladimir V. Putin, as a “killer.”

“There are a lot of killers,” Mr. Trump said in an interview on Fox News on Sunday. “You think our country’s so innocent?” The Kremlin then demanded that Fox News apologize for the host Bill O’Reilly’s characterization of Mr. Putin.

In Moscow, Mr. Kara-Murza, 35, has been in a coma and at the center of a politically hued medical mystery since Thursday as doctors puzzle over his symptoms while keeping him alive on artificial respiration.