Mr Trump has repeatedly boasted that he has the ability to end the Russia-Ukraine war if he were a president, insisting that he has a good relationship with the leaders of both countries.
“Yes please, Donald Trump — I invite you to Ukraine, to Kyiv,” Mr Zelensky said in an interview aired on Friday evening with UK broadcaster Channel 4 News.
“If you can stop the war during 24 hours, I think it will be enough to come to Kyiv, on any day I am here.”
The leader of the war-torn country said he was “frightened” at the prospect of Mr Trump returning to power due to his such speeches.
“He will make decisions on his own without — I am not even talking about Russia — but without both sides, without us,” Mr Zelensky said. “I will now talk about us. Why? Because if he says this publicly, it’s a little scary. Although I’ve seen a lot and lot of victims, but it really stresses me out a bit.
“Because it means that if his idea [of ending the war quickly], which no one has heard about, if his idea will not work for us, for our people, then he will do everything to achieve the implementation of his idea anyway. And this is what worries me a little,” he added.
In an interview with CNN last year, Mr Trump said: “If I’m president, I will have that war settled in one day, 24 hours.”
“I’ll meet with Putin. I’ll meet with Zelensky. They both have weaknesses and they both have strengths. And within 24 hours that war will be settled,” he said.
The Ukrainian president who has maintained strong ties with Democratic leader Joe Biden has remained wary of the Republican front-runner and his allies ahead of the US presidential election amid a blockade to emergency funding for Ukraine by Republicans in Congress.
During his political career, Mr Trump has over his close and friendly ties with Mr Putin and also called him “smart” for occupying “a vast, vast location, a great piece of land with a lot of people”.
Mr Trump who is leading Mr Biden in polls for a key battleground in election race, again made reference to the war in Ukraine during his speech after victory in the Republican Iowa caucus.
He said that “Russia would not have attacked” if he was still the president as he and the Russian leader “get along very well”.
Speaking in Davos last week at the World Economic Forum, Mr Zelensky brushed off fears that Mr Trump’s potential re-election would lead to reduced support for Ukraine. He said: “One man cannot change the whole nation”.
He also dismissed the idea that Mr Trump could not contain the war, saying Mr Putin “will not stop — but the question is what will the US and Trump do after this point, because in this case, it will mean that Europe lost the most useful and most strong army in Europe because we lost Ukraine”.