Zelenskiy, in a slick 21-minute New Year video greeting to his compatriots, also said only a strong Ukraine could secure peace and earn worldwide respect.
"We know that peace will not be given to us as a gift, but we will do everything to stop Russia and end the war, something each of us desires," Zelenskiy said against a backdrop of the blue-and-yellow national flag, battlefield scenes and pictures of children.
He recalled conversations with outgoing US President Joe Biden, President-elect Donald Trump and "everyone who supports us in the United States".
"I have no doubt that the new American president wants and will be able to bring peace and end (Russian President Vladimir) Putin's aggression," Zelenskiy said.
"He understands that the former is impossible without the latter. Because this is not a street brawl where the two sides need to be pacified. This is a full-scale aggression by a deranged state against a civilised one. And I believe that, together with the United States, we are capable of the strength to force Russia into a just peace."
Russia, Zelenskiy said, was not to be trusted either in battle or in talks.
"If today Russia shakes your hand, it doesn't mean that tomorrow the same hand will not start killing you," he said. "Russians fear those who are free. What they don't understand. They fear freedom."
Biden's administration has provided by far the most military support for Ukraine among Western nations since the February 2022 full-scale invasion.
Ukraine has been wary of Trump's criticism of aid to Kyiv and his pledge, during the US election campaign, to bring a quick end to the war, but Zelenskiy has expressed optimism about ensuring continuing US support.
Ukraine has endured a difficult year, with Russian forces taking village after village in a quicker advance on the eastern front than since the beginning of the invasion.
In recent months, Zelenskiy has said that any settlement to the conflict is predicated on receiving security guarantees from Western nations and Kyiv securing an invitation to join the NATO alliance, a notion Russia rejects out of hand.
In his greeting, Zelenskiy said that in the past year, Ukraine had launched an incursion into southern Russia's Kursk region, staged long-range drone strikes against distant Russian targets and developed domestically produced drones and other weapons.
"Every day in the coming year, I and all of us must fight so that Ukraine can be strong enough," he said. "Only such a Ukraine is respected and heard - both on the battlefield and at the negotiating table."
