New York (CNN) Once viewed as a routine diplomatic encounter, President Donald Trump's first formal meeting with his Ukrainian counterpart was transformed Wednesday into one of the most closely scrutinized encounters of his presidency as an impeachment crisis mounts.

Sitting in a Manhattan hotel meeting room, the men eagerly sought to deflect questions of wrongdoing after a White House transcript released earlier in the day showed Trump pressing Ukrainian President Volodymyr Zelensky to investigate Joe Biden and his son. There is no evidence of wrongdoing by either Joe or Hunter Biden.

The call has formed the basis for Democrats' impeachment probe, and has thrown Trump's presidency into turmoil. But as camera shutters whirred, Trump and Zelensky insisted nothing was untoward.

"There was no pressure," Trump insisted, denying allegations he was using his position of power to prod Ukraine into investigating a political rival.

"Nobody pushed me," Zelensky chimed in, denying he felt coerced by Trump to launch a probe. Instead, he suggested he was an unwilling participant in an American political firestorm.

"I'm sorry but I don't want to be involved (in) democratic open elections of USA," he said after consulting with a translator.

It may be too late for that. The controversy over Trump's dealings with Zelensky have massed into a political and diplomatic watershed, with Ukraine squarely in the center.

Trump remained defiant during a rambling Wednesday afternoon news conference that he "didn't threaten anybody."

"No push, no pressure, no nothing," Trump said. "It's all a hoax, folks."

Trump added, "I didn't do it. There was no quid pro quo. But there was with Biden and there was with the senators."

He said he's told House Republicans he wants "full transparency on the so-called whistleblower information," but continued to peddle conspiracy theories about Biden and his son. He also challenged the credibility of the whistleblower's claims.

Trump claimed the individual -- who has not been identified -- "didn't have any first-class or first-rate or second-tier information from what I understand."

The President told reporters he's willing to release a transcript of another, earlier call with Zelensky, as well as any calls between Ukraine and Vice President Mike Pence.

"I'll release that, too, if that's important to you," Trump said of a call which preceded the July 25 conversation the public learned more about today through a newly released transcript. "I spoke to him previous to the call that we released."

The mid-afternoon meeting between Trump and Zelensky was arranged well before the whistleblower controversy exploded into public view, according to people familiar with the plans. Aides initially did not view it as a major highlight of Trump's agenda at this week's United Nations meetings, which they expected would focus heavily on Iran and not on the questions of abuse of power.

When news emerged that an intelligence whistleblower had filed a complaint related to Trump and Ukraine -- and later that it was related to Trump's July phone call with Zelensky -- White House officials began to view the meeting as an important venue for Trump to counter Democratic accusations of wrongdoing.

Trump began by making light of the matter, telling reporters that Zelensky "made me more famous and I've made him more famous."

And later his attention seemed to drift, recalling his onetime ownership of the Miss Universe pageant, won once by a Ukrainian contestant.

But the mood turned grave as Zelensky -- himself a former television personality whose entry into politics was as unlikely as Trump's -- raised Russia's annexation of Crimea.

"If you remember, you lost Crimea during a different administration. Not during the Trump administration," Trump insisted, ascribing the invasion to his predecessor Barack Obama.

Asked whether he wants Zelensky to do more to investigate Biden, Trump said, "No, I want him to do whatever he can."

The evening before the meeting, Trump and Zelensky greeted each other at a diplomatic reception hosted by the American President for fellow leaders visiting New York for the annual United Nations meetings.

Вчора поспілкувалися з @RealDonaldTrump та @FLOTUS на Офіційному прийнятті від Президента США та Першої леді. Сьогодні продовжимо у робочому режимі! pic.twitter.com/8pnu5nHxgU — Володимир Зеленський (@ZelenskyyUa) September 25, 2019

A photo posted by Zelensky on Twitter showed the two men with their spouses smiling broadly, without a hint of the controversy that now overhangs their relationship.

There have been conversations between US and Ukrainian officials this week about the matter, including over whether to release the log of the July phone call.

One official said there had not been extensive conversations between US and Ukrainian officials about what each leader would say during the open-press part of Wednesday's meeting, though they could not rule out more informal discussions, namely between Trump and Zelensky during the diplomatic reception or between Trump's personal attorney Rudy Giuliani and his Ukrainian interlocutors.

Speaking during the meeting, Trump praised Giuliani, his private attorney, for pushing Ukrainian officials to investigate Biden, saying he was demonstrating admirable verve.

"Rudy Giuliani is a great lawyer, he was a great mayor, he's highly respected. I've watched the passion he's had on television over the last few days. Incredible what he's done," Trump said.

The sit-down between Trump and Zelensky on Wednesday was not originally meant to be their first meeting. Trump had agreed to meet Zelensky earlier this month in Poland, where he was planning to commemorate the anniversary of the outbreak of World War II.

When a hurricane forced him to cancel his plans, Mike Pence went in his place and met with Zelensky in Warsaw . Afterward, Pence was asked whether the Biden matter arose in the talks. He said no, but did turn quickly to the issue of corruption in Ukraine.

Trump and Zelensky have spoken by phone twice: once immediately following Ukrainian elections in April, and again in July. The latter conversation has become the focal point for Democrats after an intelligence whistleblower raised concerns about Ukraine and Russia.

In the months following Zelensky's election, Trump showed little interest in meeting him, believing Ukraine to be an intractably corrupt country. He ascribed Russia's annexation of part of the country to his predecessor, who he repeatedly blamed for "losing" Crimea.

But as Giuliani began raising the issue of Biden and his son, Trump's interest was piqued. He was also convinced by top national security aides, including then-national security adviser John Bolton, that engaging the new leader would be valuable in countering Russia.

Bolton was also among those aides pushing Trump to approve an aid package worth millions of dollars to Ukraine after it was put on hold. That package -- and whether it was used as a bargaining chip in Trump's attempts to push an investigation into the Bidens -- has become a lynchpin in the impeachment inquiry.