Trump's comments come after three Russian MiG-31 fighter jets entered Estonian airspace without permission on Friday, putting Europe on high alert.
US President Donald Trump said NATO member countries should shoot down Russian aircraft if they enter their airspace.
Speaking during a meeting with Ukraine's President Volodymyr Zelenskyy on the sidelines of the UN General Assembly (UNGA) in New York, Trump said "Yes, I do" when asked by journalists if countries reporting airspace violations should shoot down the aircraft in question.
Trump didn't give any further details on a NATO counteresponse to a string of airspace violations, allegedly by Russia, and stopped short of committing to US involvement in any such action.
"Depends on the circumstance," he said. "But you know, we're very strong toward NATO."
Trump's comments come after three Russian MiG-31 fighter jets entered Estonian airspace without permission on Friday. That incident happened a week after at least 19 Russian drones flew into Poland.
And on Monday night, Copenhagen and Oslo airports were closed briefly due to drones being detected near to them.
While investigations into those overflights are still under way, Denmark's Prime Minister Mette Frederiksen said Russian involvement could not be ruled out.
Ukraine can win territory back, Trump says
After his address to the General Assembly, Trump told Zelenskyy that "We have great respect for the fight Ukraine is putting up," more than three years after Russia's full-scale invasion of its neighbour.
He later posted on Truth Social that "after getting to know and fully understand the Ukraine/Russia Military and Economic situation and, after seeing the Economic trouble it is causing Russia," Trump now believes Ukraine can take back all of its territory.
"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," he wrote.
Trump was possibly referring to the 1991 borders and meant Kyiv could take back all of the territory occupied by Russia including Crimea, which Russia annexed in 2014.
"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."
This is the first time that Trump has suggested Ukraine could be capable of taking back all of its lost territory and the first time he has openly questioned Russia's military strength.
"Russia has been fighting aimlessly for three and a half years a War that should have taken a Real Military Power less than a week to win. This is not distinguishing Russia. In fact, it is very much making them look like 'a paper tiger,'" he said.
During the meeting with the US president, Zelenskyy gave Trump a battlefield update, saying Ukrainian troops had advanced some 360 kilometers in recent weeks and inflicted losses on Russia's forces.
"Thanks to our soldiers, we have this possibility, this opportunity, and we will continue until Russia will stop this war," Zelenskyy said.
He again pressed for more more international pressure on Russia to bring about an end to the war, saying "We need more pressure and more sanctions."
Addressing the UNGA earlier on Tuesday, Trump reiterated that he is ready to impose tougher sanctions on Russia but insists that all European countries should do the same.
"In the event that Russia is not ready to make a deal to end the war, then the United States is fully prepared to impose a very strong round of powerful tariffs, which would stop the bloodshed I believe very quickly," Trump said in his speech, adding that the only precondition he has is for Europe to stop purchasing Russian oil and gas.
During their talks, the US and Ukrainian presidents said they believe both Hungary and Slovakia, the two countries that have so far resisted pressure and continued to buy Russian oil, can be convinced to switch supplier.
Hungary's Foreign Minister Péter Szijjártó said on Tuesday that his country had no intention of stopping purchases or Russian oil, saying they had no infrastructure iin place to buy from anywhere else.
And Prime Minister Viktor Orbán, a close ideological ally of Trump, has also demurred about seeking energy supplies elsewhere.
"He is a friend of mine. I have not spoken to him, but I have a feeling if I did, he might stop. And I think I'll be doing that," Trump said about the Hungarian prime minister.
The meeting in New York happened as the US President's months-long efforts to broker a deal between Russia and Ukraine has yielded little in the way of results.
When asked if he still trusted Putin, Trump responded: "I'll let you know in about a month from now."