In a widely-criticised interview with Meet the Press moderator Kristen Welker, Mr Trump said that Putin’s comments proved that “what I'm saying is right” about resolving the 18-month-old war.
The former president has repeatedly claimed without providing any details that he could end the war within days should he be successful in taking back the White House.
“If I tell you exactly, I lose all my bargaining chips,” Mr Trump said during the interview broadcast on Sunday.
“I mean, you can’t really say exactly what you’re going to do. But I would say certain things to Putin. I would say certain things to [Ukrainian president Volodymyr] Zelensky,”
In remarks to the Eastern Economic Forum in Vladivostok last week, Putin said he had heard Mr Trump’s claims he would “solve all pressing problems in a few days”.
“We cannot help but feel happy about it,” the Russian president said.
However, he went on to express doubts that the Republican frontrunner for the presidential nomination could bring meaningful change to relations between the US and Russia.
“What to expect from the future, no matter who the president is, it’s hard for us to say, but it’s unlikely that anything will change radically,” Putin said.
When asked about Putin’s comments, Mr Trump told Ms Welker: “I like that he said that.
“Because that means what I’m saying is right. I would get him into a room. I’d get Zelensky into a room. Then I’d bring them together. And I’d have a deal worked out.”
Ms Welker has faced significant backlash for the interview in her first appearance since taking over NBC’s flagship political show from longtime host Chuck Todd.
The host was accused of “normalising a maniac” for providing Mr Trump with a platform to repeatedly lie with little apparent pushback.
Ms Welker instead fact-checked the former president’s claims during breaks in the interview. NBC News also published an extensive fact-check of the wide-ranging interview on Sunday.
Mr Trump has previously claimed that Putin “would have never” launched a war on Ukraine in February 2022 if he was still in power.
The former US president also claimed in a recent interview that he was “the apple” of Putin’s eye.
The pair shared a friendly relationship during Mr Trump’s term in office. During a summit in Helsinki in 2018, Mr Trump was condemned for siding with the Russian leader over his own intelligence agencies when asked whether he accepted that Moscow had interfered in the 2016 election.
During his comments last week, Putin claimed that Mr Trump’s indictments in four separate criminal investigations were evidence that the US political system was “rotten”.
“As for the prosecution of Trump, for us what is happening in today’s conditions, in my opinion, is good because it shows the rottenness of the American political system, which cannot pretend to teach others democracy,” he said.