Hoping to bolster the resolve of a nation whose heart “is covered in scars” after more than 1,000 days of unrelenting Russian assaults, President Volodymyr Zelensky of Ukraine said in his New Year’s address on Wednesday that he believed the United States would continue to stand with Kyiv in “compelling Russia into a just peace.”

He also reiterated his vow that his country would never give up on the goal of making Ukraine whole again.

“One day, Ukraine will return to be together,” Mr. Zelensky said, addressing Ukrainians living under Russian occupation in Crimea, the eastern Donbas region and the southern cities of Melitopol and Mariupol.

Despite his expression of confidence, Mr. Zelensky faces an uphill fight, not just on the battlefield, but also diplomatically.

Even Mr. Zelensky has acknowledged that it might not be possible to oust Russia solely by military means from all of the roughly 20 percent of Ukraine that it currently occupies. But he reiterated that diplomatic pressure from the West could ultimately help repel the Russian offensive led by President Vladimir V. Putin.

President-elect Donald J. Trump’s intentions for Ukraine are unclear. He has said that bringing the war to a quick end will be a priority of his administration but has not offered details on how that can be achieved. He has long made his admiration for Mr. Putin known, and has previously expressed disdain for Ukraine.