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KIEV, Ukraine – To Democrats who say that President Donald Trump's decision to freeze $391 million in military aid was intended to bully Ukraine's leader into carrying out investigations for Trump's political benefit, the president and his allies have had a simple response: There was no quid pro quo because the Ukrainians did not know assistance had been blocked.

But then on Tuesday, William Taylor, the top U.S. diplomat in Kiev, told House impeachment investigators that the freeze was directly linked to Trump's demand. That did not deter the president, who on Wednesday approvingly tweeted a quote by a congressional Republican saying neither Taylor nor any other witness had "provided testimony that the Ukrainians were aware that military aid was being withheld."

In fact, word of the aid freeze had gotten to high-level Ukrainian officials by the first week in August, according to interviews and documents obtained by the New York Times.

The problem was not bureaucratic, the Ukrainians were told. To address it, they were advised, they should reach out to Mick Mulvaney, the acting White House chief of staff, according to the interviews and records.

The timing of the communications, which have not previously been reported, shows that Ukraine was aware the White House was holding up the funds weeks earlier than acknowledged.

It also means that the Ukrainian government was aware of the freeze during most of the period in August when Trump's personal lawyer Rudy Giuliani and two American diplomats were pressing President Volodymyr Zelensky of Ukraine to make a public commitment to the investigations.

The communications did not explicitly link the assistance freeze to the push by Trump and Giuliani for the investigations. But in the communications, officials from the United States and Ukraine discuss the need to bring in the same senior aide to Zelensky who had been dealing with Giuliani about Trump's demands for the investigations, signaling a possible link between the matters.

Word of the aid freeze got to the Ukrainians at a moment when Zelensky, who had taken office a little more than two months earlier after a campaign in which he promised to root out corruption and stand up to Russia, was off balance and uncertain how to stabilize his country's relationship with the United States.

Days earlier, he had listened to Trump implore him on a half-hour call to pursue investigations touching on former Vice President Joe Biden and a debunked conspiracy theory about Ukrainian involvement in the 2016 hacking of the Democratic National Committee. Zelensky's efforts to secure a visit to the White House — a symbolic affirmation of support he considered vital at a time when Russia continued to menace Ukraine's eastern border — seemed to be stalled. U.S. policy toward Ukraine was being guided not by career professionals but by Giuliani.

Taylor testified to the impeachment investigators that he was told it was only on the sidelines of a Sept. 1 meeting between Zelensky and Vice President Mike Pence in Warsaw that the Ukrainians were directly informed by Gordon Sondland, the U.S. ambassador to the European Union, that the aid would be dependent on Zelensky giving Trump something he wanted: an investigation into Burisma, the company that had employed Biden's younger son, Hunter Biden.

American and Ukrainian officials have asserted that Ukraine learned that the aid had been held up only around the time it became public through a news article at the end of August.

As Taylor's testimony suggests, the Ukrainians did not confront the Trump administration about the freeze until they were told in September that it was linked to the demand for the investigations. The Ukrainians appear to have initially been hopeful that the problem could be resolved quietly and were reluctant to risk a public clash at a delicate time in relations between the two nations.

The disclosure that the Ukrainians knew of the freeze by early August corroborates, and provides additional details about, a claim made by a CIA officer in his whistleblower complaint that prompted the impeachment inquiry by House Democrats.

"As of early August, I heard from U.S. officials that some Ukrainian officials were aware that U.S. aid might be in jeopardy, but I do not know how or when they learned of it," the anonymous whistleblower wrote. The complainant said that he learned that the instruction to freeze the assistance "had come directly from the president," and said it "might have a connection with the overall effort to pressure Ukrainian leadership."

Publicly, Zelensky has insisted he felt no pressure to pursue the investigations sought by Trump.

"There was no blackmail," Zelensky said at a news conference this month. He cited as evidence that he "had no idea the military aid was held up" at the time of his July 25 call with Trump, when Trump pressed him for investigations into the Bidens and a debunked conspiracy theory about Ukrainian involvement in the hacking of the Democratic National Committee in 2016.

Zelensky has said he knew about the holdup of the military aid before his meeting in Poland on Sept. 1 with Pence, but has been vague about exactly when he learned about it. "When I did find out, I raised it with Pence at a meeting in Warsaw," he said this month.

In conversations over several days in early August, a Pentagon official discussed the assistance freeze directly with a Ukrainian government official, according to records and interviews. The Pentagon official suggested that Mulvaney had been pushing for the assistance to be withheld, and urged the Ukrainians to reach out to him.

The Pentagon official described Mulvaney's motivations only in broad terms but made clear that the same Ukrainian official, Andriy Yermak, who had been negotiating with Giuliani over the investigations and a White House visit being sought by Zelensky should also reach out to Mulvaney over the hold on military aid.

A senior administration official who spoke on the condition of anonymity said Monday that Mulvaney "had absolutely no communication with the Ukranians about this issue."

Ukrainian officials had grown suspicious that the assistance was in jeopardy because formal talks with the Pentagon on its release had concluded by June without any apparent problem.

In talks during the spring with American officials, the Ukrainians had resolved conditions for the release of the assistance, and believed everything was on schedule, according to Ivanna Klympush-Tsintsadze, Ukraine's former vice prime minister for Euro-Atlantic Integration.

But by early August, the Ukrainians were struggling to get clear answers from their American contacts about the status of the assistance, according to American officials familiar with the Ukrainians' efforts.

In the days and weeks after top Ukrainian officials were alerted to the aid freeze, Sondland and Kurt Volker, then the State Department's special envoy to Ukraine, were working with Giuliani to draft a statement for Zelensky to deliver that would commit him to pursuing the investigations, according to text messages between the men turned over to the House impeachment investigators.

The texts between Volker, Sondland and the top Zelensky aide did not mention the holdup of the aid. It was only in September, after the Warsaw meeting, that Taylor wrote in a text message to Sondland, "I think it's crazy to withhold security assistance for help with a political campaign."