"We're going to give a licence to you to make Patriots. That's pretty cool. This way, you can't complain that we're not giving 'em enough," Trump said at a meeting with Ukrainian President Volodymyr Zelenskiy at the NATO summit in Ankara.
"It's a defensive weapon, which I like better than an offensive weapon," Trump said.
The tone of the meeting was a sharp departure from Trump's past harsh criticism of Zelenskiy.
On Wednesday, Trump said the two had developed a "very good" relationship and that both Russia and Ukraine wanted to end the war, which began with Russia's invasion in February 2022.
Trump said he would be speaking to Russian President Vladimir Putin later on Wednesday.
Trump praised Zelenskiy, saying he had been very effective.
When asked if the United States would send additional Patriot interceptors immediately, Trump said "some" could be sent immediately and that he thought Ukraine could begin to produce its own quickly.
"We have Patriots but we don't have that many. We need them for ourselves too," the US president said.
"I think they can produce it pretty quickly. Once we explain it, we'll bring the company here. You work with the company. They have a great ability to produce weapons, pretty complex weapons."
Zelenskiy has repeatedly pleaded for the US-made interceptors - the only weapon in Ukraine's arsenal that can shoot down ballistic projectiles, whose high velocity and steep flight path make them difficult to stop.
Trump said pressure could be applied to companies to produce Patriot missiles.
"We have great power over the companies, those companies that make the Patriot," he said.
"We haven't informed the company of that yet but that'll work out all right. I'm sure they will be thrilled," Trump said.
Lockheed Martin is the prime contractor for the interceptor missiles that go in the Patriot system.
It was not clear whether missiles would be manufactured in Ukraine or in another country.
Russia fired ballistic missiles at Kyiv again overnight, officials said on Wednesday, a third attack on the Ukrainian capital in less than a week.
While Ukraine's air defences intercepted 139 of the 169 drones during the overnight strikes on the country, they were again unable to down any of the five ballistic missiles used by Russia, air force data showed.
Trump said both sides in the war would like to see it end but Putin and Zelenskiy have both been "difficult".
"We've settled a lot of wars, and this one is the one that I thought maybe would be the easiest but Putin is a difficult character, and this guy's a difficult character," Trump said, referring to Zelenskiy, who was sitting next to him.
Zelenskiy said he wanted to discuss "some very important details" with Trump.
"I'm sure you will do everything to stop this war," he told Trump.
Russia has stepped up its air war on Ukraine in recent months as its ground advances have largely stalled and Ukrainian attacks on its military logistics and oil industry triggered widespread fuel shortages.
Trump also said he thought the US would make a deal to buy Ukrainian drones.
Ukraine has developed a highly sophisticated drone industry after having only limited expertise when Russia invaded.
Ukraine has now clinched nine "drone deals" with other countries including agreements with Denmark, Estonia and the Netherlands announced on Tuesday.
