Dressed in casual clothes, Mr. Biden had a hard time sleeping during the long train ride, according to a senior official who asked not to be identified describing the trip. The president spent the ride recalling his previous trips to Kyiv, including a speech to the Ukrainian Parliament and his remarks on his final trip in 2017. He read a briefing memo on the history of Kyiv back to its founding and reflected on his history with the city.

Talking with aides, Mr. Biden recounted his telephone call with Mr. Zelensky on Feb. 24 last year as Russia’s invasion began, marveling about how the Ukrainian leader told him at the time that he was not sure when they would speak again. Now, Mr. Biden mused to aides, here they were a year later about to meet face-to-face in Kyiv.

After the all-night trip, the train pulled into Kyiv-Pasazhyrsky station at 8 a.m. local time. The platform had been cleared. On a sunny day with blue skies and a brisk chill in the air, Mr. Biden disembarked, now wearing a blue suit with a tie featuring Ukrainian colors. He was greeted by Bridget A. Brink, the American ambassador.

“It’s good to be back in Kyiv,” he said.

During his five hours in the city, he met with Mr. Zelensky at Mariinsky Palace, joined him in laying a wreath at the Wall of Remembrance at St. Michael’s Golden-Domed Monastery and stopped by the United States Embassy to meet with its staff.

Then he headed back to the same train station, departing at 1:10 p.m. On the long meandering train ride back to Poland, the senior official said the president issued a series of directions on military, economic and diplomatic areas to help Ukraine. He was seized with the meetings he had just had. Once again, he could not sleep much.

He arrived at the Przemyśl Główny station at 8:45 p.m. local time, and he headed back to the airport for a flight to Warsaw, where he will deliver a speech on Tuesday. His mind, aides said, remained on his last stop.

“Kyiv,” he had said before leaving, “has captured a part of my heart, I must say.”

Peter Baker reported from Washington, and Michael D. Shear from Warsaw.