US President Joe Biden has said that Russian President Vladimir Putin "cannot remain in power", and that Russia's war against Ukraine has been a strategic failure for Moscow.
Speaking in the Polish capital Warsaw, Mr Biden also compared Ukraine's resistance against the 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."
"In this hour, let the words of Pope John Paul burn as brightly today - never, ever give up hope, never doubt, never tire, never become discouraged. Be not afraid.
"A dictator bent on rebuilding an empire will never erase a people's love for liberty. Brutality will never grind down their will to be free. Ukraine will never be a victory for Russia, for free people refused to live in a world of hopelessness and darkness.
He continued: "We will have a different future, a brighter future, rooted in democracy and principle, hope and light, of decency and dignity, of freedom and possibilities.
"For God's sake, this man cannot remain in power."
Speaking following his speech, a White House official said Mr Biden was not calling for regime change in Russia when he made the comments.
"The President's point was that Putin cannot be allowed to exercise power over his neighbours or the region. He was not discussing Putin's power in Russia, or regime change," the official said.
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Earlier Mr Biden had spoken with top Ukrainian government officials in Warsaw, and branded Putin a "butcher" during a meeting with refugees who have fled the war in Ukraine to the Polish capital.
On the second day of a visit to Poland, Mr Biden dropped in on a meeting between Ukrainian Foreign Minister Dmytro Kuleba and Defense Minister Oleksii Reznikov, and US Secretary of State Antony Blinken and Defense Secretary Lloyd Austin.
Ukraine had received additional security pledges from the United States on developing defence co-operation, Mr Kuleba told reporters, while Reznikov expressed "cautious optimism" following the meeting with Mr Biden.
"President Biden said what is happening in Ukraine will change the history of the 21st century, and we will work together to ensure that this change is in our favour, in Ukraine's favour, in the favour of the democratic world," Mr Kuleba told Ukrainian national television
After a separate meeting with Polish President Andrzej Duda, Mr Biden reiterated Washington's "sacred" commitment to security guarantees within NATO, of which Poland is a member.
Ukraine is not a member of the Western military alliance, and the United States is wary of getting dragged into direct confrontation with Russia, but Washington has pledged to defend every inch of NATO territory.
In Warsaw, Mr Biden also visited a refugee reception centre at the national stadium. People, some waving Ukrainian flags, lined the streets as his motorcade wound its way towards the stadium.
After being greeted by celebrity chef Jose Andres, Mr Biden talked to refugees who had gathered to receive food from the World Central Kitchen NGO, asking their names and hometowns and posing for pictures with some.
More than two million people have fled the war to Poland. Altogether, about 3.8 million who have left Ukraine since fighting began on 24 February.
Asked about the impact that Putin's decision to invade Ukraine had had on the Ukrainian people, Mr Biden said the Russian leader was a "butcher".
Russia's TASS news agency quoted a Kremlin spokesman as saying Mr Biden's latest comments about Putin narrowed the prospects for mending ties between the two countries.
Putin calls Russia's military actions in Ukraine a "special military operation" to demilitarise and "denazify" the country. Russia denies targeting civilians.
Standing outside the stadium, Hanna Kharkovetz, a 27-year-old woman from the northern Ukrainian city of Kharkiv, expressed frustration that the world was not doing more to help.
"I don't know what he wants to ask us here. If Biden went to Kyiv ... that would be better than speaking here with me," she said as she waited to register her mother for a Polish national ID number.
The invasion of Ukraine has tested NATO and the West's ability to unite.
Poland was under communist rule for four decades until 1989 and was a member of the Moscow-led Warsaw Pact security alliance. It is now part of the European Union and NATO.
The rise of right-wing populism in Poland in recent years has put it in conflict with the EU and Washington, but fears of Russia pressing beyond its borders has drawn Poland closer to its Western allies.
Mr Biden's election put the nationalist Law and Justice government in an awkward position as it had set great store in its relationship with his predecessor, Donald Trump.
But as tensions with Russia rose before it invaded Ukraine, Mr Duda appeared to seek to smooth relations with Washington. In December, he vetoed legislation that critics said aimed to silence a US-owned 24-hour news broadcaster.
Mr Biden and Mr Duda were expected in their meeting to address a disagreement over how to arm Ukraine with warplanes, and other security guarantees.