The view among the national security officials was unanimous: Military aid to Ukraine should not be stopped. But the White House’s acting chief of staff thought otherwise.

That was the testimony of Laura Cooper, a Defense Department official, whose deposition was released Monday in the House impeachment inquiry of President Donald Trump.

“My sense is that all of the senior leaders of the US national security departments and agencies were all unified in their – in their view that this assistance was essential,” she said. “And they were trying to find ways to engage the president on this.”

Cooper’s testimony was among several hundred pages of transcripts released Monday, along with those of State Department officials Catherine Croft and Christopher Anderson.

Cooper told investigators that, in a series of July meetings at the White House, she came to understand that Trump’s acting chief of staff, Mick Mulvaney, was holding up the military aid for the US ally.

“There was just this issue of the White House chief of staff has conveyed that the president has concerns about Ukraine,” she testified.

When she and others tried to get an explanation, they found none.

“We did not get clarification,” she said.

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She said it was “unusual” to have congressional funds suddenly halted that way, and aides raised concerns about the legality of it. The Pentagon was “concerned” about the hold-up of funds and “any signal that we would send to Ukraine about a wavering in our commitment”, she said.

Cooper told investigators that she was visited in August by Kurt Volker, the US special envoy to Ukraine, who explained there was a “statement” that the Ukraine government could make to get the security money flowing.

It was the first she had heard of the quid pro quo that is now the central question of the impeachment inquiry – the administration’s push for the Ukraine government to investigate Trump’s political rivals.

“Somehow, an effort that he was engaged in to see if there was a statement that the government of Ukraine would make,” said Cooper, an assistant defence secretary, “that would somehow disavow any interference in US elections and would commit to the prosecution of any individuals involved in election interference.”

The House is investigating whether Trump violated his oath of office by pushing Ukraine’s president to investigate Democrats, including Joe Biden, while the administration was withholding military funds for the East European ally.

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Cooper described the Ukraine Security Assistance Initiative, saying it involved a range of items such as night-vision goggles, vehicles, sniper rifles and medical equipment.

“Security assistance is vital to helping the Ukrainians be able to defend themselves,” Cooper said.

Because Ukraine and Georgia are two “front-line states” facing Russian aggression, the US needed to “shore up these countries’ abilities to defend themselves”.

“It’s in our interest to deter Russian aggression elsewhere around the world,” she said.