Laura Cooper, the top Pentagon official overseeing U.S. policy regarding Ukraine, told House impeachment investigators last month that it was her understanding that President Donald Trump had directed the relevant agencies to freeze military aid to Ukraine over the summer, according to a transcript of her testimony released Monday.

"My secondhand understanding on this was that OMB [the White House Office of Management and Budget] wanted to communicate the president's direction to hold the assistance, and in consultation with the DOD [Department of Defense] comptroller they realized that the way to do this would be via an apportionment, this, you know, piece of guidance about the flow of funds that would tell us to hold," she said of the matter, according to the transcript.

Cooper testified that she came to this understanding in part from Michael Duffey, an associate director for national security programs at OMB, who she said conveyed in a meeting on July 26 that assistance funds from the Department of Defense and the State Department "are both affected by this hold and that it relates to the president's concerns about corruption."

Despite not usually having conversations with OMB officials, Cooper testified, she said she spoke with Duffey about a deadline to obligate the funds.

"He wanted more information on the precise nature of how long does it take to obligate, and how many cases, and that sort of thing. And I'm not a comptroller, so I referred him to the comptroller and to DSCA [the Defense Security Cooperation Agency]," she said, according to the transcript. "And it was my understanding that throughout the month of August there were many such conversations where OMB was trying to see if we could push, you know, keep planning to obligate, but keep pushing the obligations until later in the year and still complete them."

Cooper, during Oct. 23 testimony before the three House committees leading the impeachment inquiry into Trump's Ukraine dealings, also said that she had been told Trump had repeatedly expressed concerns about Ukraine and military aid to the country — weeks before the aid was frozen.

Cooper told impeachment investigators that she and other Pentagon officials had answered questions about the Ukraine assistance in the middle of June — so she was surprised when one of her subordinates told her that a hold had been placed on the funds after an interagency meeting in July 18.

“I got, you know, I got a readout from the meeting — there was discussion in that session about the — about OMB [Office of Management and Budget] saying that they were holding the Congressional Notification related to” Ukraine, Cooper testified, according to the transcript.

Cooper, according to the transcript of her testimony, described the hold as "unusual."

Cooper said that she attended a meeting on July 23, where "this issue" of Trump's "concerns about Ukraine and Ukraine security assistance" came up. She said in that meeting, the president's concerns were "conveyed" by acting White House chief of staff Mick Mulvaney.

Asked by lawmakers if the president was authorized to order that type of hold, Cooper said there were concerns that he wasn't.

"Well, I'm not an expert on the law, but in that meeting immediately deputies began to raise concerns about how this could be done in a legal fashion because there was broad understanding in the meeting that the funding — the State Department funding related to an earmark for Ukraine and that the DOD funding was specific to Ukraine security assistance. So 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," she said, according to the transcript.

At the next meeting with national security personnel, she said she told attendees "there were two legally available mechanisms should the President want to stop assistance" — a presidential rescission notice to Congress or for the Defense Department to do “a reprogramming action.”

“But I mentioned that either way, there would need to be a notification to Congress,” she said, according to the transcript.

Asked if that happened, Cooper said, "That did not occur."

In all the relevant inter-agency discussions, Cooper testified, it wasn't just Defense Department officials who believed the aid should flow to Ukraine.

"It was unanimous with the exception of the statements by OMB representatives, and those statements were relaying higher level guidance," she said, according to the transcript.

Investigators have zeroed in on the testimony of several key figures in the Ukraine affair — including Bill Taylor, the top U.S. diplomat in Ukraine, and George Kent, a deputy assistant secretary of state who worked on Ukraine and five other countries — to support the allegation that the Trump administration froze aid intended for Ukraine as part of an attempt to pressure the country to open probes that would benefit Trump politically.

The freeze on military aid to Ukraine — which Cooper’s testimony corroborates — is a crucial part of the narrative that Democrats have woven together in attempting to prove that the president sought a quid pro quo with Ukraine.

Her testimony backed up key testimony from other figures involved in the affair, including from Taylor, who testified in October that Trump directed officials to tie military aid to Ukraine to demands that the country open politically advantageous probes.

Taylor, in fact, specifically said he and others "sat in astonishment" as a White House Office of Management and Budget official said during a July 18 inter-agency call that Trump had ordered a hold on military assistance to Ukraine, according to the transcript of his testimony.

Top Republicans, including Trump himself, have said there couldn't have been a quid pro quo because, they claim, the Ukrainians were not aware that military aid was being withheld in the first place.

However, Cooper testified that she had concluded from conversations she'd had with Kurt Volker, the then-U.S. special envoy to Ukraine, and Taylor, that that couldn't possibly be true.

"I knew from my Kurt Volker conversation and also from sort of the alarm bells that were coming from Ambassador Taylor and his team that there were Ukrainians who knew about this," she said, according to the transcript.

Cooper also testified that there was a concerted effort within the executive branch to try to get the president to lift the hold.

“My sense is that all of the senior leaders of the U.S. national security departments and agencies were all unified in their — in their view that this assistance was essential, that we could work with the government of Ukraine to tackle corruption, and they were trying to find ways to engage the President on this,” Cooper said.

She said she discussed the frozen aid with Volker on Aug. 20.

"So in that meeting he did mention something to me that, you know, was the first about somehow an effort that he was engaged in to see if there was a statement that the government of Ukraine would make that would somehow disavow any interference in U.S. elections and would commit to the prosecution of any individuals involved in election interference. And that was about as specific as it got," she said.

The transcript of Cooper's closed-door testimony was just the latest document made public as the probe moves to a new phase. House Democrats last week released transcripts of testimony from Taylor, Kent, Volker, U.S. Ambassador to the European Union Gordon Sondland and ousted U.S. ambassador to Ukraine Marie Yovanovitch.

The testimony of those key figures have largely established a narrative that suggests the Trump administration sought to tie the nearly $400 million in military and security aid to Ukraine as well as the prospect of a coveted White House meeting to demands that Volodymyr Zelenskiy announce probes into former Vice President Joe Biden and his son Hunter Biden and a conspiracy related to the 2016 election.

In a statement, the chairs of the three committees leading the inquiry — House Intelligence Committee Chair Adam Schiff, D-Calif.; House Foreign Affairs Committee Chair Eliot Engel, D-N.Y.; and House Oversight Committee acting Chair Carolyn Maloney, D-N.Y. — said Cooper testified that Trump "through the Office of Management and Budget, directed the freeze on hundreds of millions of dollars of critical military aid for Ukraine, against the judgment of career officials in the Department of Defense, Department of State, and other relevant agencies."

They also said that she had "raised concerns, as did others on several occasions, to senior U.S. government officials about the legality of withholding the congressionally-authorized money, and the challenges that White House delays would put on spending it."

Cooper's testimony was delayed by five hours after a group of House Republicans who don't sit on the committees that questioned her stormed the secure room where her deposition was taking place.