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A key Pentagon official told House impeachment investigators that former US special envoy to Ukraine Kurt Volker told her Ukrainian officials were alarmed in August that US security aid was being held up — an indication Kiev was aware of the delay earlier than it was reported publicly, according to a deposition transcript released Monday.

Laura Cooper, the Pentagon’s deputy assistant secretary for Russia, Ukraine and Eurasia, told lawmakers behind closed doors last month that she met with Volker in August to discuss the hold on aid. She said Volker told her in their meeting that he was attempting to lift the hold on the aid by having the Ukrainians deliver a public statement that they would launch the investigations being sought by President Donald Trump.

She described Volker seeking a statement from the Ukrainians about opening investigations into election interference that would trigger a release in the aid.

“I knew from my Kurt Volker conversation and also from sort of the alarm bells that were coming from Ambassador (Bill) Taylor and his team that there were Ukrainians who knew about this,” Cooper said, describing the Ukrainians as aware of the freeze on aid in August 2019. “The context for the discussion that I had with Ambassador Volker related specifically to the path that he was pursuing to lift the hold would be to get them to make this statement, but the only reason they would do that is because there was, you know, something valuable.”

Cooper’s deposition was one of three transcripts released Monday by House Democrats. They also made public the interviews last month of two former deputies of Volker, Catherine Croft and Christopher Anderson.

According to his opening statement, Anderson told lawmakers last month that then-national security adviser John Bolton cautioned about the influence Trump’s personal lawyer Rudy Giuliani had on US-Ukraine policymaking during a meeting in mid-June with top US officials.

Cooper’s interview transcript provides new detail about how the Ukrainians learned that $400 million in security aid was held up, even before it was reported in late August. While her testimony does not contain major revelations or accusations that hit at the core of the Democrats’ impeachment case, her interview provided lawmakers with technical details about how the aid was held up — and how the Ukraine hold diverged from the norm.

Cooper testified that at a meeting on July 26 — the day after Trump’s phone call with Ukrainian President Volodymyr Zelensky — it first became clear to her that the military aid to Ukraine that was affected by the hold was related to the President’s concerns about corruption and that “immediately deputies began to raise concerns about how this could be done in a legal fashion.”

“The comments in the room at the deputies’ level reflected a sense that there was not an understanding of how this could legally play out. And at that meeting the deputies agreed to look into the legalities and to look at what was possible,” Cooper added.

Cooper testified that individuals at the Department of Defense and other agencies believed Ukraine was making progress in combatting corruption, enough to continue providing the aid being challenged by OMB.

“It was unanimous with the exception of the statements by OMB representatives, and those statements were relaying higher level guidance,” Cooper said.

Cooper has been the only Pentagon witness to testify so far as part of the House Democratic impeachment inquiry into Trump and Ukraine. She testified the day that a group of House Republican lawmakers barged into the House Intelligence Committee secure spaces to protest the Democratic-run impeachment inquiry. The stunt, which was led by GOP Rep. Matt Gaetz of Florida, delayed her deposition for five hours.

Volker deputy testifies: Giuliani’s involvement ‘was an obstacle to improving relations’

Anderson, a State Department employee who was one of the two former Volker deputies testifying, on the same day last month, said that Volker told him he didn’t think Giuliani would move on from the Ukraine issue.

“I understood what he was saying, that if we … shouldn’t hope that he’lI focus on something else and move on to another issue, he’s going to keep raising this issue,” Anderson said of the President’s personal attorney.

Anderson said it was his understanding that Volker believed Giuliani’s involvement “was an obstacle to improving relations and putting pressure on Russia.”

Anderson, who served at the US Embassy in Kiev from 2014-2017, testified that they saw former Vice President Joe Biden “as one of the lead policy people on Ukraine, that he was sort of very focused on Ukraine.”

Croft testified that she was “trepidatious” about accepting the job as special assistant to Volker because “it was possible that the Trump administration would choose to change its policy to suit domestic politics.”

Croft said she “speculated” in a conversation with Taylor about the effect of a potential Biden candidacy, that “it seemed logical to me that in an attempt to counter the narrative about Russian support for the Trump administration in the 2016 election or Russian interference in the 2016 election that … it would be useful to shift that narrative by shifting it to Ukraine as being in support of the Clintons.”

She thought that “painting sort of Ukraine as being against Trump would help distract from a narrative or balance out a narrative that he had gotten help in the 2016 election from Russia.”

Croft also testified about how then-Office of Management and Budget Director Mick Mulvaney held up plans to send Ukraine Javelin anti-tank missiles in late 2017, despite the fact that “all of the other policy agencies were in support.” The Javelins were ultimately provided to Ukraine.

Croft testified that Mulvaney, now the acting White House chief of staff, was involved in Ukraine policy this year, including working with US Ambassador to the European Union Gordon Sondland.

Former White House aide Fiona Hill and National Security Council Ukraine expert Lt. Col. Alexander Vindman testified that Sondland told them he was coordinating Ukraine policy with Muvlaney. While Croft did not cite specific examples of Mulvaney’s influence, she said she knew that Sondland and Mulvaney were in touch because Sondland’s staff would tell her that. Sondland “somehow knew him,” she said of Mulvaney.

This story has been updated with additional developments Monday.

CNN’s Kevin Liptak, Maegan Vazquez, Jennifer Hansler and Zachary Cohen contributed to this report.