Donald Trump has said he believes Ukraine can win back all of the territory Russia has taken since its invasion.
In a change in rhetoric, the US President made the comment on his Truth Social platform soon after meeting Volodymyr Zelensky.
President Trump wrote: "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.
"With time, patience, and the financial support of Europe and, in particular, Nato, the original Borders from where this War started, is very much an option."
Mr Zelensky has been pushing Trump to show more support for Kyiv's war effort, including by imposing tough new sanctions on Russia.
Many Ukrainians were shocked when Trump gave Russian President Vladimir Putin red carpet treatment at a mid-August summit in Alaska, and believe Moscow will not stop its war unless it faces heavy external pressure.
In the post, Trump criticised Russia, saying it had been fighting "aimlessly" in a war that a "real military power" would have won in less than a week.
However, he has not imposed tougher sanctions and he and his aides have seemed to indicate that Kyiv must cede both Crimea and parts of eastern Ukraine to Russia in order to end the conflict.
Volodymyr Zelensky and Donald Trump held a meeting at the United Nations
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In his post on Tuesday, however, Mr Trump hinted at stronger action. "Putin and Russia are in BIG Economic trouble, and this is the time for Ukraine to act," the post said.
President Trump said the US will continue to supply weapons to allies "for Nato to do what they want with them."
Mr Zelensky said he had discussed Russia's stuttering economy during a meeting with Mr Trump that he said was constructive.
The Ukrainian President said there was an understanding that Mr Trump was ready to provide security guarantees after the war ends, adding that assistance from Washington could be a "game-changer" for Ukraine.
LATEST FROM THE FRONTLINE IN UKRAINE
The Ukrainian leader was at the 80th United Nations General Assembly in New York City
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In the backdrop of these meetings, Nato has warned Russia that it would use "all necessary military and non-military tools" to defend itself as it condemned Moscow for violating Estonian airspace in "a pattern of increasingly irresponsible behaviour".
The warning came after Estonia said that three Russian MiG-31 fighter jets violated its airspace for 12 minutes before Italian fighter jets escorted them out.
The week before, around 20 Russian drones entered Polish airspace, prompting Nato jets to shoot some of them down and the alliance to beef up the defence of Europe's eastern flank.
Asked whether Nato countries should shoot down Russian aircraft that enter their airspace, Mr Trump told reporters: "Yes, I do."
The two presidents held a bilateral meeting in New York
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Nato soldiers held exercises with Polish forces after the drone attack
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Estonia invoked Article 4 of Nato's founding treaty, which states that allies will "consult together whenever, in the opinion of any of them, the territorial integrity, political independence or security" of a member is threatened.
It is only the ninth time in Nato's 76-year history that the article has been invoked, two of those occasions have come this month in response to the incidents over Poland and Estonia.
Russia said Estonia's assertion that Russian jets violated Estonian airspace was unfounded and accused Tallinn of seeking to ratchet up East-West tensions.
On the Polish incident, Russia said its drones had carried out a major attack on military facilities in western Ukraine that night but had not planned to hit targets in Poland.
The Kremlin warned against Estonia seeking to ratchet up East-West tensions
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A Nato spokesman said: "Russia bears full responsibility for these actions, which are escalatory, risk miscalculation and endanger lives. They must stop," the council said in a statement.
"Russia should be in no doubt: Nato and Allies will employ, in accordance with international law, all necessary military and non-military tools to defend ourselves and deter all threats from all directions."
The recent incidents have prompted calls from some European politicians for Nato to shoot down manned Russian fighters that intrude on the alliance's airspace.
German Defence Minister Boris Pistorius warned against such talk, saying: "Reckless demands to shoot something out of the sky or to send a specific message of strength do not help in this situation. We need to be calm, clear and prudent, and act appropriately."