And it delivered: their appearance before the media in New York was tense, bizarre and funny all at the same time.
On the right: Trump, 73, the onetime real estate mogul and reality television star, now the Republican president of the United States.
On the left: Zelensky, 41, a onetime comedian, now president.
In the middle: a giant arrangement of green and white flowers.
Trump met a dozen world leaders during his trip to the Big Apple for the annual United Nations General Assembly. But his handshake with the Ukrainian president was the only game in town on Wednesday.
A summer telephone conversation between the two men is at the center of a political firestorm in the US capital, and prompted opposition Democrats to launch an impeachment inquiry against POTUS 45.
In his usual dark blue suit and red tie, Trump -- literally sitting on the edge of his seat -- was anything but relaxed.
Zelensky, sporting a three-piece black suit, seemed far less anxious and settled easily into his armchair.
- 'Tremendous potential' -
The tension in the room was palpable, but the conversation started on a lighter note, and even seemed like a surreal comedy act.
"He's made me more famous and I've made him more famous," the billionaire Trump quipped at the start of the meeting, to laughs from the press corps.
"It's better to be on TV than by phone," Zelensky replied with a bit of a knowing grin, speaking in English, a language in which he was fairly comfortable.
"It's a country, I think, with tremendous potential," Trump said, using a phrase he has employed to refer to numerous nations, from North Korea to Iran.
"Yes, I know it, because I am from that country," deadpanned Zelensky, who came to prominence playing a president on television.
Trump -- somewhere between amusement and confusion -- smiled.
- Come visit me -
Zelensky pressed Trump to commit to a visit to Ukraine, recalling -- though visibly conscious of the sensitive nature of the comparison -- that Trump's predecessor Barack Obama had never made the trip.
"Well, I'm going to try," answered the cagey US president.
Zelensky recalled that Trump had invited him to Washington and then added with a smile: "I think you forgot to tell me the date."
Finally, the tone got a bit more serious.
Zelensky, who was a teenager during Ukraine's drive for independence in the early 1990s, hammered home what matters to him: "to stop the war in Donbass," a separatist-held region in eastern Ukraine.
- 'In other words, no pressure' -
And then the journalists became part of the play, bombarding the two men with questions.
The tone shifted significantly.
Did the leader of the world's only superpower put pressure on his Ukrainian counterpart to investigate the family of Joe Biden, one of the Democrats vying to take on Trump in the 2020 election?
Zelensky hesitated and stammered before answering: "I think you read everything. (...) I'm sorry, but I don't want to be involved in the democratic, open elections of (the) USA."
Then he was more precise: "We had -- I think (a) good phone call. It was normal. We spoke about many things, and... so I think, and you read it, that nobody pushed me."
Trump chimed in: "In other words, no pressure."
And then the Republican leader got angry.
After all, a single word -- impeachment -- had ruined his day in his hometown.
Was he angry about the potential miscalculation of releasing a memo detailing his conversation with Zelensky? Only time will tell.
But in the meeting with Zelensky, his frustration burst out in the open.
"We have corruption also. Mr President," he told the Ukrainian.
"We have a lot of corruption in our government and when you see what happened with Hillary Clinton..." Trump said before launching into a list of his political enemies and their alleged wrongdoing.
And what about the role of Trump's personal attorney, Rudy Giuliani, in his dealings with Ukraine? The president was steadfast.
"Rudy Giuliani's a great lawyer, he was a great mayor. He's highly respected," Trump said.
When asked his thoughts about House Speaker Nancy Pelosi, the leader of the Democrats on Capitol Hill, Trump was unequivocal: "She's lost her way, she's been taken over by the radical left."
"Nancy Pelosi, as far as I'm concerned, unfortunately, she's no longer speaker of the House," he added.
A few minutes later, in a brief exchange with journalists, Trump said his talks with Zelensky had gone well, and said the Ukrainian had cleared up the matter by saying he had not been pressured in any way.
In a press conference, Trump described the entire scandal surrounding the call as a "hoax" and a "witch hunt."
The impeachment inquiry has only just begun.
AFP / Andrew CABALLERO-REYNOLDS 
AFP/File / Olivier Douliery 
AFP/File / SAUL LOEB, MANDEL NGAN 