(CNN) In a significant reversal, a top US diplomat revised his testimony to impeachment investigators to admit a quid pro quo linking US aid to Ukraine with an investigation into President Donald Trump's political rival.

US Ambassador to the European Union Gordon Sondland on Monday sent the committees a three-page addition to his testimony, saying he had remembered a September 1 conversation in which he told a top aide to Ukrainian President Volodymyr Zelensky that the security aid was linked to investigations into former Vice President Joe Biden and the 2016 election.

"I now recall speaking individually with Mr. (Andriy) Yermak, where I said 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 said.

Sondland's new testimony, which was included in the public release of his closed-door deposition transcript on Tuesday, adds to Democrats' evidence that the President connected the freezing of US security aid to Ukraine to investigations into Biden as well as the hacking of the Democratic National Committee's servers during the 2016 election, which cuts to the heart of their impeachment case against Trump. The committees have now heard from several witnesses, including top US diplomat in Ukraine Bill Taylor and National Security Council aide Tim Morrison, who have testified that Ukraine opening such investigations was linked to $400 million in US security aid and a one-on-one meeting between Trump and Zelensky.

The House Intelligence, Foreign Affairs and Oversight committees released deposition transcripts of Sondland and former US Special Envoy to Ukraine Kurt Volker on Tuesday as they shifted toward the public phase of their impeachment inquiry.

In his deposition last month, Sondland testified that he did not ultimately know why the aid to Ukraine was withheld. But he told lawmakers that efforts by the President's personal attorney Rudy Giuliani to persuade Ukraine to open an investigation into Trump's political rivals "kept getting more insidious" as time went on, and he suggested Giuliani's efforts might have been illegal, according to the deposition transcript.

Sondland testified that it would be "improper" for Giuliani to push the Ukrainians to investigate Biden or get involved in the 2020 election. Asked if it was illegal, Sondland said: "I'm not a lawyer, but I assume so."

In his own testimony, Volker said that the Ukrainians had asked to be put in touch with Giuliani — whose efforts have been described by other witnesses as a shadow foreign policy outside of State Department channels — because they believed "that information flow would reach the President." He said he had been surprised and troubled by what was said on the July 25 call between Trump and Zelensky.

Still, Volker's testimony also provided Trump and his allies with fodder, as they've been pushing for it to be released publicly. Volker told lawmakers that he didn't know about any "quid pro quo" linking US military assistance to the announcement of Ukrainian investigations into Biden and the Democrats.

"You asked what conversations did I have about that quid pro quo, et cetera," Volker said. "None, because I didn't know that there was a quid pro quo."

He testified that after learning about the holdup of US military aid, he had worked to get the assistance resumed, and that he had never believed it was linked to Trump's desire for a probe of the Bidens.

Volker also said that the Ukrainians didn't know about the holdup of military assistance until after the Trump administration stopped pressing them to announce an investigation into the Bidens. This testimony bolsters a key tenet of Trump's defense -- that there was no "quid pro quo" with Ukraine because the new government in Kiev was not aware that military aid was being withheld.

"To my knowledge, the news about a hold on security assistance did not get into Ukrainian government circles, as indicated to me by the current foreign minister, then diplomatic adviser, until the end of August," Volker said. "And by the time that we had that, we had dropped the idea of even looking at a statement."

White House press secretary Stephanie Grisham said in a statement that Sondland had testified he did not know why the Ukraine aid was frozen, and that Volker "confirms there could not have been a quid pro quo because the Ukrainians did not know about the military aid hold at the time."

But Volker appeared to be unaware that on September 1, Sondland had told Zelensky's political aide that the security aid and the announcement of a public investigation were in fact linked.

House Democrats have now released transcripts from four of the 13 closed-door depositions they've conducted thus far as they shift toward public hearings, which could begin as soon as next week, in the impeachment inquiry.

Volker and Sondland, along with Energy Secretary Rick Perry, had dubbed themselves the "three amigos" who handled US-Ukraine policy. Text messages provided to Congress by Volker, who resigned last month as the Ukraine scandal was unfolding, show his exchanges with Giuliani and senior State Department diplomats. He denied participating in any effort to dig up political dirt on Biden, but the texts revealed that he had talked to Ukrainian officials about launching politically charged investigations.

Democrats seek clarification from Sondland

The revision of Sondland's testimony this week comes after Democrats had been calling on him to clarify his closed-door testimony following his deposition on October 17. Sondland's initial testimony appears to have been contradicted by at least two other witnesses, according to CNN reporting and publicly released statements.

At the heart of the discrepancy, which his clarification appears to be attempting to address, is whether Sondland ever explicitly linked US actions to requests for Ukraine to launch investigations into the Bidens, and whether he had dangled White House visits or US military aid as a potential quid pro quo.

In his October testimony, Sondland said the President had told him directly that "there is no quid pro quo," which prompted him to tell Taylor that his suggestion that US aid was linked to investigations was inaccurate.

Sondland explained that on a September 9 phone call with Trump, the President told him: "I want nothing. I want no quid pro quo. I want Zelensky to do the right thing."

"And I said: 'What does that mean?' And he said: 'I want him to do what he ran on.' And that was the end of the conversation. I wouldn't say he hung up on me, but it was almost like he hung up on me," Sondland added.

Sondland told the House committees that he eventually became aware that Ukraine aid was held up to entice Ukrainian corruption investigations, and eventually realized the investigations were linked to the Bidens.

"Finally at some point I made the Biden-Burisma connection, and then the transcript was released," Sondland said during his testimony. He said he couldn't remember specific dates, and for some time hadn't made the connection between the Bidens and Burisma, the Ukrainian natural gas company for which Hunter Biden sat on the board.

Sondland described "a continuum," beginning with a May 23 meeting and "ending up at the end of the line when the transcript of the call came out."

"It started as talk to Rudy, then others talk to Rudy," he explained. "Corruption was mentioned. Then, as time went on— and, again, I can't nail down the dates — then let's get the Ukrainians to give a statement about corruption. And then, no, corruption isn't enough, we need to talk about the 2016 election and the Burisma investigations."

Sondland's testimony includes other discrepancies with Trump officials who have come before the committee. His description of a July 10 meeting with then-national security adviser John Bolton, for instance, is at odds with the testimony of former White House Russia adviser Fiona Hill , who said the meeting was "abruptly terminated and that angry words were used."

Sondland said that was contrary to his memory, and he wondered if he "slept through something."

Sondland also described his work with Giuliani that was documented in the text messages Democrats released last month between US diplomats, Giuliani and the Zelensky aide.

Sondland discussed how the effort by Giuliani and others to prompt Ukraine to make a public announcement about its investigation would need to be on TV so Trump would see it.

"I think this was the press statement had now morphed into some kind of an interview that President Zelensky would give to a TV station," Sondland told the committees.

When asked what network the statement should be made on, he answered, "I don't know, but something President Trump would obviously see." He then mentioned Fox and its host Tucker Carlson -- prompting laughter in the committee room, according to the transcript.

Sondland acknowledged in the testimony that he had spoken to Perry ahead of his deposition to "refresh my memory." And he said he also had spoken briefly to the President during a White House gathering, where Trump told him to "go tell the truth."

Former US envoy illuminates key meeting

Volker's testimony provided more detail into his efforts to work with Giuliani, Sondland and the Ukrainians amid the push for Ukraine to open an investigation and the freezing of US security aid.

Volker testified that the holdup of aid "struck me as unusual." He said he became aware of the hold on aid on July 18 -- before the Trump-Zelensky call -- but did not find out the reason the aid had been frozen.

"Nobody ever gave a reason why," Volker said.

He said that in a May 23 meeting with Trump in which the President directed his aides to "talk to Rudy" about Ukraine, Volker and other administration officials recommended Trump schedule an Oval Office meeting with the newly elected Ukrainian President. But Trump was skeptical.

"They are all corrupt, they are all terrible people," Volker recalled Trump saying. "I don't want to spend any time with that."

Volker said that he told Zelensky and another Ukrainian official about the "Giuliani factor" -- that the President's personal lawyer was amplifying a "negative narrative" about Ukraine.

"I explained it to President Zelensky and Chief of Presidential Administration, Andriy Bohdan, was standing next to him. And I explained that I thought that there is a negative narrative about Ukraine that is counteracting all the good things that he is doing, and that we are officially communicating back, and that this is being amplified by Rudy Giuliani," Volker told.

Still, Volker testified that he never felt like Giuliani did anything against US interests, breaking with other witnesses like Hill. In fact, Volker believed Giuliani was helping to advance US interests, and that's why he put the Ukrainians in touch.

Volker said he thought it was "probably very helpful" that he had mentioned this to Zelensky prior to his call with Trump on July 25.

After Volker and Sondland proposed that Zelensky announce an investigation that mentioned Burisma and the 2016 election, Volker said, he advised the Ukrainians to drop a public announcement after learning that the Justice Department had not requested probes into the 2016 election and Burisma, despite what Giuliani was promoting.

"It died. I mean, no one — once we started seeing a tempo of engagement with Ukraine, we had first the sense that Rudy was not going to be convinced that it meant anything, and, therefore, convey a positive message to the President if it didn't say Burisma and 2016," Volker said. "I agreed with the Ukrainians they shouldn't do it, and in fact told them just drop it, wait till you have your own prosecutor general in place. Let's work on substantive issues like this, security assistance and all. Let's just do that. So we dropped it."

Volker testified that he had personally told Giuliani that the source of many of those theories was "not credible." Giuliani has spent much of this year spreading theories about former Biden and the Democrats peddled by former Ukrainian Prosecutor General Yuriy Lutsenko.

This story has been updated with additional developments Tuesday.