President Biden and Polish President Andrzej Duda, right, meet on Tuesday in Warsaw.  Evan Vucci/Associated Press

WARSAW, Poland — President Biden on Tuesday warned of “hard and bitter days ahead” as Russia’s invasion of Ukraine nears the one-year mark, but vowed that no matter what, the United States and allies “will not waver” in supporting the Ukrainians.

A day after his surprise visit to Kyiv, Biden used a strongly worded address in neighboring Poland to praise allies in Europe for stepping up over the past year and to send a clear message to Russian President Vladimir Putin that “NATO will not be divided, and we will not tire.”

“One year ago, the world was bracing for the fall of Kyiv,” Biden said before a crowd of thousands outside Warsaw’s Royal Castle. “I can report: Kyiv stands strong. Kyiv stands proud. It stands tall and, most important, it stands free.”

With Russia and Ukraine each preparing spring offensives, Biden insisted there will be no backing down from what he’s portrayed as a global struggle between democracy and autocracy – though polling suggests American support for ongoing military assistance appears to be softening.

“Democracies of the world will stand guard over freedom today, tomorrow and forever,” Biden declared. The U.S. and allies will “have Ukraine’s back.”

Biden’s speech came a day after his unannounced trip to Kyiv, where he met with Ukrainian President Volodymyr Zelensky and walked the city streets as an air raid siren blared.

Last year, weeks after Russian forces began their attacks on Ukraine, Biden delivered a harsh condemnation of Putin from the gardens of the castle. Speaking Tuesday to a crowd that included Polish citizens and Ukrainian refugees – and millions more following in Ukraine, Russia and around the world – he made his case that Putin’s war has been a failure.

President Biden stands with children after delivering a speech marking the one-year anniversary of the Russian invasion of Ukraine, on Tuesday at the Royal Castle Gardens in Warsaw. Evan Vucci/Associated Press

“When President Putin ordered his tanks to roll into Ukraine, he thought we would roll over. He was wrong,” Biden said.

The president also declared “the democracies of the world have grown stronger” while the world’s autocrats – including Putin – have become weaker.

“Autocrats only understand one word – no, no, no,” Biden said. “No, you will not take my country. No, you will not take my freedom. No, you will not take my future.”

Biden was using the trip to prepare allies for an ever-more-complicated stage of the war and to reassure allies in the region that the U.S. was committed for the long haul. He met Tuesday with Moldovan President Maia Sandu — who last week claimed Moscow was behind a plot to overthrow her country’s government using external saboteurs — and with his host Polish President Andrzej Duda.

“We have to have security in Europe,” Biden said at the presidential palace. “It’s that basic, that simple, that consequential.”

He described NATO as “maybe the most consequential alliance in history,” and he said it’s “stronger than it’s ever been” despite the Russian leader’s hopes that it would fracture over the war in Ukraine.

Duda praised the American president’s visit to Kyiv as “spectacular,” saying it “boosted morale of Ukraine’s defenders.”

He said the trip was “a sign that the free world, and its biggest leader, the president of the United States, stands by them.”

On Wednesday, Biden will meet again with Duda along with other leaders of the Bucharest Nine, the easternmost members of the NATO military alliance. Ukraine is not a member.

While Biden was in Poland, Putin announced that Moscow would suspend its participation in the last remaining nuclear arms control pact with the United States.

The New START Treaty caps the number of long-range nuclear warheads countries may deploy and limits the use of missiles that can carry atomic weapons.

Despite his criticisms of Putin, Biden did not mention the START suspension during his speech. And the Russian Foreign Ministry later said that, despite Putin’s announcement, it would continue abiding by the treaty’s caps.

The conflict in Ukraine – the most significant war in Europe since World War II – has already left tens of thousands of people dead, devastated Ukraine’s infrastructure system and damaged the global economy.

President Biden and Ukrainian President Volodymyr Zelensky walk at St. Michaels Golden-Domed Cathedral during an unannounced visit, in Kyiv, Ukraine, on Monday. Evan Vucci/Associated Press

While Biden is looking to use his whirlwind trip to Europe as a moment of affirmation for Ukraine and allies, the White House has also acknowledged that there is no clear endgame to the war in the near term, and the situation on the ground has become increasingly complex.

The administration on Sunday said it has new intelligence suggesting that China, which has generally remained on the sidelines of the conflict, is now considering sending Moscow lethal aid. Secretary of State Antony Blinken said it could become a “serious problem” if Beijing follows through.

Biden and Zelensky discussed capabilities that Ukraine needs “to be able to succeed on the battlefield” in the months ahead, said U.S. National Security Adviser Jake Sullivan. Zelenskyy has been pushing the U.S. and European allies to provide fighter jets and long-range missile systems known as ATACMS – which Biden has declined to provide so far. Sullivan declined to comment on whether there was any movement on that during the leaders’ talk.

With no quick end in sight for the war, the anniversary is a critical moment for Biden to try to bolster European unity and reiterate the West’s position that Putin’s invasion was a frontal attack on the post-World War II international order. The White House hopes the president’s visit to Kyiv and Warsaw will help bolster American and global resolve.

In the U.S., a poll published last week by the Associated Press-NORC Center for Public Affairs Research showed that support for providing Ukraine with weapons and direct economic assistance is softening. And earlier this month, 11 House Republicans introduced what they called the “Ukraine fatigue” resolution urging Biden to end military and financial aid to Ukraine, while pushing Ukraine and Russia to come to a peace agreement.

Biden dismissed the notion of waning American support during his visit to Kyiv.

President Biden delivers a speech marking the one-year anniversary of the Russian invasion of Ukraine, on Tuesday at the Royal Castle Gardens in Warsaw. Evan Vucci/Associated Press

“For all the disagreement we have in our Congress on some issues, there is significant agreement on support for Ukraine,” he said. He described the conflict as “about freedom of democracy at large.”

Biden had high praise for Poland’s efforts to assist Ukraine. More than 1.5 million Ukrainian refugees have settled in Poland since the start of the war, and millions more have crossed through Poland on their way to other countries. Poland has also provided Ukraine with $3.8 billion in military and humanitarian aid, according to the White House.

The Biden administration announced last summer that it was establishing a permanent U.S. garrison in Poland, creating an enduring American foothold on NATO’s eastern flank.

“The truth of the matter is the United States needs Poland and NATO as much as NATO needs the United States,” Biden told Duda on Tuesday.

Miller and Megerian reported from Washington. Associated Press writers Monika Scislowska in Warsaw, Evan Vucci in Kyiv and Kevin Freking in Washington contributed.