Volodymyr Zelensky was invited to Washington after Biden disappointed Ukraine by waiving most sanctions on the Nord Stream 2 pipeline being built from Russia to Germany
White House press secretary Jen Psaki said the leaders had discussed the countries' "shared democratic values and Ukraine's Euro-Atlantic aspirations."
"The Russian president once said that if a fight is inevitable, you need to hit first. But every leader needs to understand that a fight must not be inevitable when it concerns a real war and millions of human lives."
The Ukrainian military on Thursday announced that another of its soldiers had been killed, bringing to 25 the number of troops killed since the start of the year, compared with 50 in all of 2020.
Zelensky said on Monday that Ukraine, one of the poorest countries in Europe, would begin the first phase of the vaccination campaign later this month.
She reiterated the president's appeal to Brussels and said the bloc should do more to help the ex-Soviet country which relies heavily on European backing.