Around a quarter of Ukrainians have been driven from their homes, including a tenth of the population that has fled abroad.
Zelenskiy said the military situation in the south and east was "still very difficult".
"The successes of our military on the battlefield are really significant, historically significant. But they are still not enough to clean our land of the occupiers. We will beat them some more," he said in a late-night video address.
Zelenskiy has appealed to Biden for the United States to designate Russia a "state sponsor of terrorism," joining North Korea, Cuba, Iran and Syria, the Washington Post reported.