Combined images of Russian President Vladimir Putin and US. President Joe Biden.
Biden compared Ukraine's resistance against a Russian invasion to the anti-Soviet "battle for freedom" and said the world must prepare for a "long fight ahead".
"We stand with you," he told Ukrainians.
Addressing ordinary Russians, he said that they were "not our enemy" and urged them to blame Putin for the heavy economic sanctions imposed by the West.
He also warned Russia not to move on an "inch" of NATO territory, reiterating the "sacred obligation" of collective defence for alliance members.
At the start of his address in the Polish capital's Royal Castle, he echoed the words of late pope John Paul II telling Ukrainians: "Be not afraid."
At the conclusion of his sweeping address, he said: "We will have a different future, a brighter future rooted in democracy and principle, hope and light.
"For God's sake, this man cannot remain in power," he said.