MOSCOW — Russia has become the first country in the world to approve a vaccine for the coronavirus, President Vladimir V. Putin announced on Tuesday, though global health authorities say the vaccine has yet to complete critical, late-stage clinical trials to determine its safety and effectiveness.

Mr. Putin, who told a cabinet meeting on Tuesday morning that the vaccine “works effectively enough,” said that his own daughter had taken it. And in a congratulatory note to the nation, he thanked the scientists who developed the vaccine for “this first, very important step for our country, and generally for the whole world.”

The major powers are locked in a global race for a vaccine that President Trump, Mr. Putin and China’s president, Xi Jinping, are treating as a proxy war for their personal leadership and competing national systems. The United States, with an effort called Operation Warp Speed, and China have poured billions into the pursuit, and health officials worry that Russia is trying to snatch a victory by cutting corners.