In a midnight social media post, President Trump called Dmitri A. Medvedev a “failed former President of Russia” who had better “watch his words.”

Less than three hours later — morning by then in Moscow — Mr. Medvedev responded. He said Mr. Trump should picture the apocalyptic television series “The Walking Dead” and referred to the Soviet Union’s system for launching a last-ditch, automatic nuclear strike.

“Russia is right about everything and will continue to go its own way,” said Mr. Medvedev’s post on the Telegram messaging app.

It was the second time this summer that Mr. Trump and Mr. Medvedev, Russia’s head of state from 2008 to 2012, traded blows on social media.

The exchanges have been striking not only for the verbal brinkmanship on display between the world’s nuclear superpowers, but also for the mismatched stature of the figures involved. While Mr. Trump commands the world’s most powerful military, Mr. Medvedev is widely seen as a social-media attack dog relegated to the periphery of President Vladimir V. Putin’s inner circle.

The viciousness of the overnight exchange highlighted the volatility and opacity of a geopolitical relationship in which Mr. Trump and Mr. Putin set policy largely on their own. And it put on display the combustible mix that can occur when the Kremlin’s longstanding willingness to use nuclear threats meets Mr. Trump’s penchant for late-night diatribes on the internet. Hanging in the balance is the future of Ukraine, three years into Russia’s full-scale invasion.