KYIV, Ukraine — To Democrats who say that President Donald Trump’s decision to freeze a $391 million military aid package to Ukraine 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 could not have been any quid pro quo because the Ukrainians did not know the assistance had been blocked.

Following testimony by William B. Taylor Jr., the top U.S. diplomat in Ukraine, to House impeachment investigators on Tuesday that the freezing of the aid was directly linked to Trump’s demand for the investigations, the president took to Twitter Wednesday morning to approvingly quote a Republican member of Congress saying neither Taylor nor any other witness had “provided testimony that the Ukrainians were aware that military aid was being withheld.”

But 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 a bureaucratic glitch, the Ukrainians were told then. 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 about the issue, which have not previously been reported, shows that Ukraine was aware the White House was holding up the funds weeks earlier than U.S. and Ukrainian officials had acknowledged. And it 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 Zelenskiy of Ukraine to make a public commitment to the investigations being sought by Trump.

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 Zelenskiy who had been dealing with Giuliani about Trump’s demands for the investigations, signaling a possible link between the matters.

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Word of the aid freeze got to the Ukrainians at a moment when Zelenskiy, 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 hack of the Democratic National Committee. Zelenskiy’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 told the impeachment investigators that it was only on the sidelines of a Sept. 1 meeting in Warsaw between Zelenskiy and Vice President Mike Pence that the Ukrainians were directly told the aid would be dependent on Zelenskiy giving Trump something he wanted: an investigation into Burisma, the company that had employed Hunter Biden, Joe Biden’s son.

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 story at the end of August.

The aid freeze is getting additional scrutiny from the impeachment investigators on Wednesday as they question Laura K. Cooper, a deputy assistant defense secretary for Russia, Ukraine and Eurasia. This month, Democrats subpoenaed both the Defense Department and the White House Office of Management and Budget for records related to the assistance freeze.

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.

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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 sparked 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, Zelenskiy has insisted he felt no pressure to pursue the investigations sought by Trump.

“There was no blackmail,” Zelenskiy said at a news conference earlier 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.

Zelenskiy 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.

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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 Zelenskiy should also reach out to Mulvaney over the hold on military aid.

A senior administration official who was not authorized to speak publicly about the issue said on 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, Gordon D. Sondland, the U.S. ambassador to the European Union, and Kurt D. Volker, then the State Department’s special envoy to Ukraine, were working with Giuliani to draft a statement for Zelenskiy to deliver that would commit him to pursuing the investigations, according to text messages between the men turned over to the House impeachment investigators.

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The text messages between Volker, Sondland and the top Zelenskiy 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.”

After being informed on Sept. 1 in Warsaw that the aid would be released only if Zelenskiy agreed to the investigations, Ukrainian officials, including their national security adviser and defense minister, were troubled by their inability to get answers to questions about the freeze from U.S. officials, Taylor testified.

Through the summer, Zelenskiy had been noncommittal about the demands from Volker, Sondland and Giuliani for a public commitment to the investigations. On Sept. 5, Taylor testified, Zelenskiy met in Kyiv with Sens. Ron Johnson, R-Wis., and Chris Murphy, D-Conn.

Zelenskiy’s first question, Taylor said, was about the security aid. The senators responded, Taylor said, that Zelenskiy “should not jeopardize bipartisan support by getting drawn into U.S. domestic politics.”

But Sondland was still pressing for a commitment from Zelenskiy, and was pressing him to do a CNN interview in which he would talk about pursuing the investigations sought by Trump.

Zelenskiy never did the interview and never made the public commitment sought by the White House, although a Ukrainian prosecutor later said he would “audit” a case involving the owner of the company that paid Hunter Biden as a board member.

Giuliani has said he had nothing to do with the assistance freeze and did not talk to Trump or “anybody in the government” about it. “I didn’t know about it until I read about it in the newspaper,” he said in an interview last week.