NEW YORK — President Trump opened his must-see-TV meeting with Ukrainian President Volodymyr Zelensky on Wednesday with a self-aware joke.

Somehow, the Miss Universe pageant and Hillary Clinton’s missing emails soon came up, but not until after Trump had disarmed the crowd with a bit of the old razzmatazz.

“He’s made me more famous and I’ve made him more famous,” Trump said to startled laughter in a bland hotel conference room lined with Cabinet officials.

In the back were reporters poised to shout questions about whether the president had improperly leaned on the new Ukrainian leader to seek out dirt on one of Trump’s leading challengers for reelection.

A White House transcript of a phone call between the two leaders had been released hours earlier, recording Trump asking Zelensky for “a favor.” The call is now at the center of an impeachment inquiry announced Tuesday by House Speaker Nancy Pelosi (D-Calif.) and marks the latest wrenching plot shift in Trump’s operatic tenure.

“We spoke a couple times, as you probably remember,” Trump cracked.

“And they’d like to hear every single word, and we give them every single word, and then they’ll say, ‘Well, about today?’ ” Trump said.

“I think the press would probably like to stay in the meeting, but we have lots of witnesses,” he continued, an apparent reference to the Cabinet officials in the room as well as the phalanx of White House staff that records, transcribes and annotates conversations like the one he had in July.

Zelensky, a comedian and television star before he was elected this year, also tried to keep the mood light by noting that “it’s better to be on TV than by phone, I think.”

On paper, Trump’s day Wednesday looked like a normal, busy presidential trip to the annual U.N. meeting. He convened leaders to talk about the plight of Venezuela, signed a preliminary trade agreement with Japan and met with the leader of El Salvador in addition to the headliner sit-down with Zelensky.

But the fast-moving story regarding the phone call, the subsequent whistleblower complaint and the unfolding impeachment inquiry dominated the day as it has dominated Trump’s entire stay here, which will wrap up Thursday morning. For as much as Trump complained that the rest of his agenda is ignored in favor of what he labeled “a hoax,” he animated it with further unsubstantiated claims Wednesday that Biden’s son, Hunter Biden, had improperly profited from his father’s government role with business dealings in Ukraine and China.

Democrats said the transcript reveals a brazen effort by Trump to jump-start corruption investigations he hoped could hurt Biden, and to link Zelensky’s compliance with U.S. military aid Trump had put on hold.

Hunter Biden served for nearly five years on the board of Burisma, Ukraine’s largest private gas company, whose owner came under scrutiny by Ukrainian prosecutors for possible abuse of power and unlawful enrichment.

Hunter Biden was not accused of any wrongdoing in the investigation. As vice president, Joe Biden pressured Ukraine to fire its top prosecutor, Viktor Shokin, who Biden and other Western officials said was not sufficiently pursuing corruption cases. At the time, the investigation into Burisma was dormant, according to former Ukrainian and U.S. officials.

Standing alongside Trump, Zelensky insisted Wednesday that “nobody pushed me” to investigate.

“I think you read everything,” Zelensky said as he and Trump faced the cameras.

“I’m sorry, but I don’t want to be involved” in U.S. elections, Zelensky continued, as Trump smiled beside him. “No, you heard that we had, I think, good phone call. It was normal.”

Trump chimed in: “In other words, no pressure.”

The meeting on the sidelines of the annual U.N. General Assembly was arranged before The Washington Post first reported a whistleblower complaint about Trump’s behavior with a foreign leader who turned out to be Zelensky.

A copy of the whistleblower complaint was delivered to Congress on Wednesday, in between Trump’s meeting with Zelensky and a news conference closing out his packed three days of diplomacy here.

“I didn’t pressure anybody,” Trump said at the news conference, which began with a rambling opening monologue that included references to his promised border wall with “anti-climb panels” and a complaint about “unelected bureaucrats” who stymie his agenda.

Trump kept the Zelensky meeting on his schedule and stuck to the plan to have reporters witness the first few minutes as part of a nothing-to-see-here-folks approach. He had a willing partner in Zelensky, although the young leader appeared a bit pained.

Zelensky repeatedly tried to steer the conversation back to his priorities — the anticorruption platform that got him elected and the five-year-old proxy war with Russia in his country’s east. He said he wants to reclaim Crimea, the territory Russia seized in 2014.

Trump’s praise for that agenda and for Ukraine itself took an odd turn when he said — falsely — that a Ukrainian contestant won the Miss Universe contest when he owned it. An Associated Press fact check notes that a Ukrainian woman has never won the Miss Universe title, although several finished in the top 10 during Trump’s tenure from 1996 to 2015.

Trump also noted, “If you remember, you lost Crimea during a different administration, not during the Trump administration.”

“Yeah. So you have chance to help us,” Zelensky responded, perhaps sensing that Trump might take things in a dark direction.

“That’s right. I do. But that was during the Obama administration that you lost Crimea, and I didn’t think it was something that you should have,” Trump said. “But that was done a long time ago, and I think it was handled poorly. But it’s just one of those things.”

Trump frequently holds a mirror to his predecessor’s administration to make the claim that he is performing better. Although he claims Obama’s weakness allowed Russia to take Crimea, he also suggests that it is settled business.

As he has elsewhere, Trump used the sit-down with Zelensky to claim that while Obama sent his country “pillows and sheets” to help fend off Russian aggression, he is sending antitank weaponry.

“Boy, that was a nice question. I like that question,” he said to laughter when a reporter asked whether deleted email messages from Clinton’s tenure as secretary of state might reside somewhere in Ukraine.

Trump mused that indeed they might, and repeated his charge that Clinton was trying to hide something.

“How she got away with that one is just — but it’s one of many. And it’s corrupt government. Because we have corruption also, Mr. President,” he told Zelensky. “We have a lot of corruption in our government.”