Editor's note: This is a developing story and will update with more details of the testimony.

Updated 6 p.m. ET

Gordon Sondland, the U.S. ambassador to the European Union, acknowledged telling an aide to Ukraine's president that U.S. military aid was tied to a public statement of "corruption" from Kyiv, according to a supplemental statement from Sondland that was part of a transcript released Tuesday of the envoy's closed-door deposition Oct. 17 before congressional investigators.

President Trump, through a pressure campaign led by his personal lawyer Rudy Giuliani, wanted Ukraine to investigate debunked conspiracy theories related to the 2016 election and the actions of former Vice President Joe Biden and his son Hunter, which the president and his supporters say amount to corruption.

"I said that resumption of U.S. aid would likely not occur until Ukraine provided the public anti-corruption statement that we had been discussing for many weeks," Sondland writes, noting that he now recalls a Sept. 1 meeting in which he told that to an aide to Ukrainian President Volodymyr Zelenskiy.

That conversation followed a meeting between Vice President Pence and Zelenskiy, "in which President Zelensky had raised the issue of the suspension of U.S. aid to Ukraine directly with Vice President Pence," Sondland notes.

The pressure campaign evolved over time, Sondland said, questioning its legality.

"It kept — it kept getting more insidious as timeline went on," Sondland said, "and back in July, it was all about just corruption."

In addition to Sondland's deposition, the House committees leading the impeachment inquiry into Trump also released the transcript of their interview with Kurt Volker, the former U.S. special envoy to Ukraine. (Read Volker's transcript here and Sondland's here.)

It is the second batch of transcripts released in a new more public-facing phase of the inquiry, which so far has been conducted behind closed doors.

"Pompeo rolled his eyes"

Sondland also revealed that Secretary of State Mike Pompeo was aware of Giuliani's irregular role. Sondland said he discussed Giuliani's involvement in foreign affairs with Pompeo. Pompeo's reaction?

"Pompeo rolled his eyes and said: Yes, it's something we have to deal with," Sondland said.

Volker also said Pompeo was aware of Giuliani's influence on Trump.

"I described my concern that [Giuliani] is projecting a damaging or a negative image about Ukraine, and that's reaching the President, and that I am trying to work with Ukrainians to correct that messaging, correct that impression," Volker said.

According to Volker, Pompeo said he was "glad" Volker was trying to correct those efforts.

The question of quid pro quo

The White House contends that the transcripts of the depositions help the president.

"Both transcripts released today show there is even less evidence for this illegitimate impeachment sham than previously thought," White House press secretary Stephanie Grisham said in a statement, referring to the impeachment inquiry. "Ambassador Sondland squarely states that he 'did not know, (and still does not know) when, why or by whom the aid was suspended.' He also said he 'presumed' there was a link to the aid — but cannot identify any solid source for that assumption.

"By contrast, Volker's testimony confirms there could not have been a quid pro quo because the Ukrainians did not know about the military aid hold at the time. No amount of salacious media-biased headlines, which are clearly designed to influence the narrative, change the fact that the President has done nothing wrong."

At the heart of the inquiry is whether the president sought a quid pro quo from his Ukrainian counterpart for his own political gain. Trump denies he set any conditions on releasing Ukrainian aid. But in testimony released Tuesday, Sondland told investigators that he told Zelenskiy on July 19 that his call was Trump "is finally on, and I think it's important that you, you know, give President Trump — he wanted this — some kind of statement about corruption."

Trump's desire for a public statement from Ukraine's president is similarly detailed by the testimony of acting U.S. ambassador to Ukraine William Taylor in his opening statement during his deposition late last month.

"Ambassador Sondland also told me that he now recognized that he had made a mistake by earlier telling the Ukrainian officials to whom he spoke that a White House meeting with President Zelenskyy was dependent on a public announcement of investigations," Taylor said. "In fact, Ambassador Sondland said, 'everything' was dependent on such an announcement, including security assistance. He said that President Trump wanted President Zelenskyy 'in a public box' by making a public statement about ordering such investigations."

Taylor noted that he told Sondland to push back against the president's "demand" and "should have more respect for another head of state."

For his part, Volker said the holdup of military aid "was not significant" in the grand scheme of things.

"I don't believe — in fact, I am quite sure that at least I, Secretary Pompeo, the official representatives of the U.S., never communicated to Ukrainians that it is being held for a reason. We never had a reason," he testified.

Sondland contradictions

Sondland, a major Trump donor, was in contact with the president and was part of a campaign to get Ukraine to investigate the Bidens' business dealings in the country. Multiple witnesses had contradicted Sondland's original testimony that he was not aware of the broader strategy, which Sondland amended in this new release.

Another point of contention in Sondland's testimony is that he said that a July 10 National Security Council meeting was uneventful, while others said the meeting was problematic because of what they saw as pressure leveled by Sondland.

Sondland had said he only talked broadly during that meeting about investigations by Ukraine. The three witnesses said then-national security adviser John Bolton quickly shut the meeting down. Fiona Hill, a former top Russia adviser on the NSC, said Bolton described what was happening as a "drug deal" and described the president's lawyer Giuliani as a "hand grenade" who was going to blow everyone up.

In his prepared testimony to the committees on Oct. 17, Sondland wrote that "neither Ambassador Bolton, Dr. Hill, nor anyone else on the NSC staff ever expressed any concerns to me about our efforts, any complaints about coordination between State and the NSC, or, most importantly, any concerns that we were acting improperly."

The top Ukraine expert on the NSC, Lt. Col. Alexander Vindman, testified that he did raise his concerns directly to Sondland.

Sondland also said he was kept out of the broader plan to pressure Ukraine to investigate Democrats in exchange for aid and engagement with the White House.

In his testimony, Sondland said, "Withholding foreign aid in order to pressure a foreign government to take such steps would be wrong. I did not and would not ever participate in such undertakings."

Testimony by Taylor and others appeared to contradict Sondland's insistence in his opening statement that he was unaware of such a campaign.

Ukrainian prosecutor's allegations

Volker noted in his testimony that former Ukrainian prosecutor Yuriy Lutsenko, in an attempt to curry favor with Trump, peddled false allegations about the 2016 election and the Bidens' connections to Ukraine.

"My opinion of Prosecutor General Lutsenko was that he was acting in a self-serving manner," Volker said, "frankly making things up, in order to appear important to the United States, because he wanted to save his job."

Volker is not alone. Taylor and his predecessor as U.S. ambassador to Ukraine, Marie Yovanovitch, also testified that Lutsenko's allegations were not credible.

And yet, Volker testified that he thought Trump did believe Lutsenko's allegations, which partially led to Yovanovitch's recall.

"Yes, it is my opinion that he believed them," Volker said. "I know that Mr. Giuliani did, and I know that Mr. Giuliani reported to President Trump. So I believe that President Trump believed them."

In other words, the last two U.S. ambassadors to Ukraine and the U.S. special envoy to Ukraine all determined that Lutsenko's allegations were false, and yet the president of the United States apparently made consequential moves based on Lutsenko's allegations.

The allegations against potential political rival Joe Biden, if true, had the potential to help Trump's reelection campaign.

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