U.S. Ambassador to the European Union Gordon Sondland amended his previous closed-door testimony with House impeachment investigators to say that he told a top Ukrainian political aide that the release of U.S. security aid was conditioned on Ukraine publicly announcing an investigation that would help President Donald Trump politically.

Sondland's attorney sent the committee a letter and a three-page addition to his testimony, which said he had remembered a conversation on September 1 with Andriy Yermak, an aide to the Ukrainian President, linking the aid to the investigations, CNN reports.

"I now recall speaking individually with Mr. 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.

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Sondland's new testimony, which was included in the public release of his closed-door deposition transcript on Tuesday, adds to Democrats' evidence that U.S. President Donald Trump connected the freezing of $400 million in U.S. security aid to Ukraine to investigations into the 2016 election and former Vice President Joe Biden.

The House Intelligence, Foreign Affairs and Oversight Committees released deposition transcripts of Sondland and former U.S. special envoy to Ukraine Kurt Volker on Tuesday as they shift to the public phase of the impeachment investigation.

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Sondland testified that he did not ultimately know why the aid to Ukraine was withheld. He told lawmakers that efforts from 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 an excerpt of his closed-door 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 testimony, Volker provided more detail into the May 23 meeting with Trump in which the President directed his aides to "talk to Rudy" about Ukraine. In that meeting, Volker and other administration officials recommended Trump schedule an Oval Office meeting with the newly elected Ukrainian President Volodymyr Zelensky. 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 he became aware of the hold on aid on July 18 – before the Trump-Zelensky call – but he did not find out the reason for the hold.

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

After conducting closed-door depositions for several weeks, House Democrats have started to release transcripts of those interviews as they move toward the next phase of the inquiry. They plan to hold open hearings with some key witnesses, which would give them a platform to publicly make the case against Trump before voting on articles of impeachment.