He visited Washington DC to hold a private meeting with Republican and Democratic leaders on Thursday, warning that his country would “lose the war” without US support.
President Zelensky faced questions about the latest round of US funding, an additional 24 billion US dollars, that hangs in the balance.
The US has for 19 months helped Mr Zelensky’s troops in the fight against Russia’s invasion.
But a faction of congressional Republicans, largely aligned with Donald Trump, is threatening to disrupt what has been easy sign-offs on four previous rounds of funding for Ukraine, totalling 113 billion US dollars (£92 billion).
Asked about the funding issue after meeting with Mr Zelensky, US President Joe Biden said: “I’m counting on the good judgment of the United States Congress. There’s no alternative.”
He gave Mr Zelensky a red carpet arrival on the White House South lawn and made clear his concern with Congress.
It was Mr Zelensky’s second visit to Washington since Russia invaded Ukraine in February 2022.
The administration did announce another 325 million US dollars (£264 million) on Thursday in what’s known as presidential drawdown assistance for Ukraine.
US Secretary of State Antony Blinken said the package would include additional air defense, artillery ammunition, cluster munitions and other arms.
Mr Zelensky thanked Mr Biden for the new military aid package, saying “it has exactly what our soldiers need now”.
Mr Biden told Mr Zelensky: “Mr President, we’re with you, we’re staying with you”, before reaching across the table and shaking his hand after two hours of talks.
Lawmakers who attended the private meeting described questioning Mr Zelensky on the way forward for Ukraine’s counteroffensive, as the fight to roll back invading Russian forces moves closer to the two-year mark without major breakthroughs in Russia’s heavily mined lines.
Mr Zelensky “conceded that it’s tough, very tough to overcome entrenched defenses,” Independent Senator Angus King said.
“They believe they will make slow but steady progress, but it’s not going to be quick.”
On Friday Mr Zelensky arrived in Canada to address its Parliament and meet with Prime Minister Justin Trudeau in Ottawa.
Canada is one of Kyiv’s staunchest supporters and is set to announce during the visit that it is sending more weapons to Ukraine, according to a government official.
“Canada will continue to support Ukraine as long as it takes and we will always stand firm to defend the rule of law and the international rules based order,” Mr Trudeau told reporters in New York on Thursday.
Meanwhile Mr Zelensky faces challenges in Europe, with Poland’s prime minister saying his country is no longer sending arms to Ukraine amid a dispute over grain imports.