A White House official who was on President Trump Donald John TrumpFederal prosecutor speaks out, says Barr 'has brought shame' on Justice Dept. Former Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick MORE's call with Ukrainian President Volodymyr Zelensky told Congress there was “no doubt” that Trump had invoked a quid pro quo, according to transcripts released Friday as part of Democrats' impeachment inquiry.

Lt. Col. Alexander Vindman, a Ukraine specialist on the National Security Council (NSC) who was on the July 25 phone call, told House lawmakers the message from Trump was clear.

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"The demand was, in order to get the White House meeting, they had to deliver an investigation,” Vindman testified.

That assessment was backed by Fiona Hill, formerly Trump’s top Russia analyst at the NSC, who told lawmakers it was widely understood that investigating Burisma — the Ukrainian energy giant that had employed former Vice President Joe Biden Joe BidenFormer Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick Bloomberg rolls out M ad buy to boost Biden in Florida MORE’s son Hunter Biden — was code for investigating the Bidens.

Vindman said Trump mentioned Burisma by name on the July 25 call.

“This is very much repeating things that Rudy Giuliani Rudy GiulianiThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting CIA found Putin 'probably directing' campaign against Biden: report Democrats fear Russia interference could spoil bid to retake Senate MORE was saying in public on television,” Hill said.

Both Vindman and Hill told House investigators last month that Giuliani, the president's personal attorney, was a liability to diplomats managing U.S. foreign policy in Kiev — and should therefore be avoided.

Vindman said he told Kurt Volker Kurt VolkerGOP senators request details on Hunter Biden's travel for probe Yovanovitch retires from State Department: reports Live coverage: Senators enter second day of questions in impeachment trial MORE, former special envoy to Ukraine, on “a couple occasions” that “there was a lot of risk involved with trying to deal with Mr. Giuliani,” according to the transcript of his Oct. 29 deposition.

And Hill said she’d given Volker similar advice, warning it wasn’t “a good idea” to meet with the former New York City mayor, whose multifaceted agenda in Ukraine included efforts to oust a veteran U.S. diplomat; pressure Ukrainian leaders to find dirt on Trump’s political rivals; and drum up business opportunities for his financial partners.

“[Volker] said that he thought that he would be able to … reason with him and to, you know, kind of … manage this,” Hill said. “Well, we did not think that this was manageable.”

That view was shared by John Bolton John BoltonJudge appears skeptical of Bolton's defense of publishing book without White House approval Maximum pressure is keeping US troops in Iraq and Syria Woodward book trails Bolton, Mary Trump in first-week sales MORE, Trump’s former national security adviser, who had characterized Giuliani as “a hand grenade” who would ultimately “blow everybody up,” Hill testified.

“Ambassador Bolton had said repeatedly that nobody should be meeting with Giuliani,” Hill said during her deposition on Oct. 14.

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But the isolation campaign met with limited success for one simple reason: Trump, in an Oval Office meeting in May, had told several top diplomats — including Volker and Gordon Sondland, Trump’s ambassador to the E.U. — that Giuliani would be his point man on Ukrainian policy.

“He just kept saying, ‘Talk to Rudy, talk to Rudy,'” Sondland told lawmakers during his deposition last month.

Volker testified that he did just that, delivering a warning to Giuliani that he shouldn’t trust a former Ukrainian prosecutor, Yuriy Lutsenko, whom the State Department had long considered to be corrupt and self-serving. But the message fell flat, and Giuliani, Volker testified, emerged as “a problem” for diplomats seeking to root out corruption and strengthen ties with Kiev.

“The negative narrative about Ukraine which Mr. Giuliani was furthering was the problem,” Volker testified on Oct. 3. “It was impeding our ability to build the relationship the way we should be doing.”

Aside from his association with Lutsenko, Giuliani was also in contact with John Solomon, an opinion columnist, formerly with The Hill, who wrote a series of pieces earlier this year promoting allegations of corruption by Biden, as well as debunked theories that Ukraine leaked information in 2016 about then-Trump campaign chairman Paul Manafort Paul John ManafortFBI official who worked with Mueller raised doubts about Russia investigation Our Constitution is under attack by Attorney General William Barr Bannon trial date set in alleged border wall scam MORE in an effort to bolster Democratic presidential nominee Hillary Clinton Hillary Diane Rodham ClintonBloomberg rolls out M ad buy to boost Biden in Florida Hillicon Valley: Productivity, fatigue, cybersecurity emerge as top concerns amid pandemic | Facebook critics launch alternative oversight board | Google to temporarily bar election ads after polls close Trump pledges to make Juneteenth a federal holiday, designate KKK a terrorist group in pitch to Black voters MORE.

Another Solomon column, based on an interview with Lutsenko, accused Marie Yovanovitch, the former U.S. ambassador to Ukraine, of providing Lutsenko with a “do-not-prosecute” list. Vindman testified that there wasn’t a shred of truth to that account.

"All the key elements were false,” he said, adding, "his grammar might have been right."

The new details emerged this week as Democrats leading the impeachment investigation shift from weeks of closed-door depositions to a public phase of the process, to feature several televised hearings next week. As part of that transition, they’re releasing the verbatim transcripts of the 15 witness depositions they’ve conducted privately since the inquiry was launched on Sept. 24.

The transcripts for Vindman and Hill were the latest releases in that process. Both of them provided new ammunition for Democrats, who have accused Trump of abusing his office in pressing Zelensky to open investigations into the 2016 elections and Biden — both of which would have helped Trump politically heading into the 2020 elections.

Hill also testified that Giuliani — along with a pair of business partners with Ukrainian ties, Lev Parnas and Igor Fruman — were tapping Giuliani’s proximity to Trump in order to boost their own financial prospects.

“My view in looking at this, is that individuals — private individuals like Mr. Giuliani and his business associates — are trying to appropriate presidential power or the authority of the president, given the position that Mr. Giuliani is in, to also pursue their own personal interests,” she said.

Giuliani was also eroding morale in the State Department, multiple diplomats have testified, particularly after he helped to orchestrate the removal of Yovanovitch, who was recalled to Washington in May. Hill called it “a real turning point” for the diplomatic corps.

“There was no basis for her removal,” Hill testified. “The accusations against her had no merit whatsoever. This was a mishmash of conspiracy theories.”

Giuliani’s attorneys did not respond Friday to questions seeking comment.