In the long and grueling war in Ukraine, emotions can swing wildly between hope and despair. But President Trump’s sudden reversal on Tuesday in how he views the war — he said Ukraine could win it — suggested such a major shift that many Ukrainians were unsure how to process it.

Whereas he once pressed Ukraine to take any deal or risk losing even more territory, Mr. Trump said on Truth Social that he now believed that Ukraine could not only survive Russia’s onslaught but also eventually win and retake all its land. He painted a picture of a Russian economy teetering on collapse and said the Russian army looked like a “paper tiger.”

His comments were met in Ukraine with a mix of gratitude and caution, shaped by experience. Even President Volodymyr Zelensky, while welcoming the statement, said he was “a little bit” surprised by its strength.

Ostap Yarysh, a well-known Ukrainian commentator, said on Facebook that “Trump’s statement on Ukraine yesterday was certainly the most favorable we’ve heard so far” but that it was “too early to talk about a White House strategy overhaul or a radical shift in the president’s thinking, although there is such a temptation.”

Many Ukrainians seemed not to take President Trump’s post seriously or joked that it could change at any moment. “What happens next may be as written, or it may be the other way around,” Viktor Shlinchak, the head of the Institute of World Policy, an analytical research group, said on Facebook.

Moscow, predictably, dismissed Mr. Trump’s comments. “Russia is more associated with a bear, and there are no paper bears,” the Kremlin spokesman, Dmitri S. Peskov, said.

Just months ago, Mr. Trump berated Mr. Zelensky in the Oval Office, telling him he had “no cards” to play. Since then, there have been many twists in Mr. Trump’s public comments on the war. But when he greeted Russia’s president, Vladimir V. Putin, on a red carpet in Alaska this summer, breaking years of diplomatic isolation, it seemed Moscow had shaped his view.

After a three-hour meeting with Mr. Putin, Mr. Trump insisted that Ukraine would ultimately have to give up territory.

But after his meeting on Tuesday with Mr. Zelensky on the sidelines of the United Nations General Assembly, Mr. Trump said he now fully understood the military and economic dynamics of the war and had changed his outlook.

“I think Ukraine, with the support of the European Union, is in a position to fight and WIN all of Ukraine back in its original form,” Mr. Trump said on Truth Social. He added that Russia was “in BIG Economic trouble” and this was “the time for Ukraine to act.”

It is unclear how realistic Mr. Trump’s latest assessment of possible victory is. Mr. Zelensky and top Ukrainian military commanders have previously said there is no purely military way to reclaim the roughly 20 percent of Ukrainian territory occupied by Russian forces, barring an unexpected Russian collapse.

Mr. Trump himself now says he expects the war to be long.

Mr. Zelensky said after his meeting with Mr. Trump that he had spoken about battlefield developments, and he told Fox News that U.S. and Ukrainian intelligence assessments were largely aligned.

Before leaving Kyiv for the United Nations gathering in New York, Mr. Zelensky said Ukraine had taken back about 360 square kilometers in September, a claim supported by combat footage verified by military analysts.

“It’s not a big victory, but it means we are not losing,” Mr. Zelensky said on Fox. “This is important.”

Still, Russia’s personnel advantage gives it an edge in a war of attrition. And even as Ukrainian forces pushed Russians back in some areas of the front in recent weeks, Russian soldiers pressed forward elsewhere.

Russia has occupied more than 1,150 square miles of land in Ukraine so far this year, according to DeepState, a Ukrainian group that charts battlefield movements. It also drove the Ukrainian forces out of its own Kursk region. But despite its efforts this year, Russia failed to capture many Ukrainian strongholds it had been trying for, including Pokrovsk.

Mr. Zelensky also argues that Russia is suffering economically, with international sanctions, rising war costs and Ukrainian strikes on fuel infrastructure.

That argument seems to have resonated with Mr. Trump, who referred in his social media post on Tuesday to Russia’s economic troubles and long lines at gas stations.

When the Kremlin launched its invasion nearly four years ago, it expected a short war to seize Ukraine. It now believes a long conflict favors Russia, banking on its large population, industrial capacity and determination to win regardless of cost.

From Moscow’s view, Mr. Zelensky’s openness to talks with Russia is a sign of weakness and progress toward the Kremlin’s achieving its goals.

Mr. Putin is also betting his wartime economy can hold out.

Though the economy is not “crashing” as Mr. Trump said in his meeting with Mr. Zelensky, Russia’s military spending has strained the budget. The deficit has reached $50 billion, bringing proposals to raise taxes for defense funding.

On Wednesday, Mr. Peskov denied deep economic troubles, citing Russia’s resilience.

Ukrainian drone strikes have caused fuel shortages in parts of Russia, but unemployment is near historic lows, and incomes have risen.

Mr. Trump’s current view may not endure. But even if he has changed his thinking, the Trump administration has made it clear that he does not view the war as critical to America’s national security interests.

Ukrainians have learned to be wary of words unsupported by action.

Mr. Zelensky, during an appearance before the U.N. Security Council on Tuesday, talked about the failure of the 1994 Budapest Memorandum, which was designed to protect Ukraine’s security in exchange for nuclear disarmament. He cited it as evidence that “international promises can turn into blabbering.”

“That is why today, with Britain, with France and already with more than 30 nations in our coalition of the willing, we are building a new security architecture,” he said, referring to attempts to provide Ukraine with some security guarantees. “We count on the United States of America as a backstop.”

An American backstop is probably the best Kyiv can hope for at the moment.

When Mr. Trump ended his Truth Social statement outlining his views on the war, he signed off in a way that signaled that he may see himself as something of a bystander now.

“Good luck to all!” Mr. Trump wrote.

Maria Varenikova contributed reporting.