Top Ukraine diplomat Bill Taylor testified Tuesday that he was told a military aid package to Ukraine had been withheld by President Donald Trump pending an agreement by that country to launch investigations into Trump's political rivals.

Taylor said Gordon Sondland, U.S. ambassador to the European Union, told him that Trump said he wants Ukraine's president "to state publicly that Ukraine will investigate [natural-gas company Burisma Holdings] and alleged Ukrainian interference in the 2016 election," according to a copy of Taylor's opening statement published Tuesday by The Washington Post.

"'Everything' was dependent on such an announcement, including security assistance," Sondland said, Taylor testified in the closed-door hearing with House lawmakers conducting an impeachment inquiry into the president.

Trump has repeatedly denied that there was any quid pro quo involving the hundreds of millions of dollars in aid allocated to Ukraine, the delivery of which had been delayed for months by the Trump administration without a clear explanation at the time. That military assistance was eventually delivered in September.

Democrats leaving the secure hearing room earlier in the day told NBC News that Taylor was among the most credible witnesses yet to be heard in the impeachment inquiry. Taylor's testimony drew a "direct line" connecting the foreign aid to Ukraine with the political investigations called for by Trump, Rep. Debbie Wasserman Schultz, D-Fla., told NBC.

The House probe was launched in the wake of a whistleblower's complaint that raised alarms about the president's July 25 call with Ukraine President Volodymyr Zelensky, when Trump asked Zelensky to "look into" unsubstantiated corruption allegations against former Vice President Joe Biden and his son Hunter. Trump had also asked Zelensky in that call to "do us a favor though" and investigate Ukraine's alleged role regarding interference in the 2016 presidential election.

Taylor's opening statement said that in August and September, he "became increasingly concerned that our relationship with Ukraine was being fundamentally undermined by an irregular, informal channel of U.S. policy-making and by the withholding of vital security assistance for domestic political reasons."

Trump and his lawyer, former New York Mayor Rudy Giuliani, have alleged that Joe Biden helped his family profit off his role as Barack Obama's vice president, in part through Hunter Biden's employment on the board of Burisma. They suggest that the elder Biden improperly pressured Ukraine to fire a prosecutor there out of concern that he would investigate the natural gas company.

There is no credible evidence that Biden's actions as vice president were intended to help his son, as many Western leaders had called on Ukraine at the time to fire that prosecutor over allegations of corruption. Hunter Biden has not been credibly accused of illegal wrongdoing related to his work with the company; he says he did "nothing wrong at all."

The Trump administration has vowed not to cooperate with the impeachment inquiry, which is being led by the House Intelligence, Oversight and Foreign Affairs committees. The administration has reportedly tried to block current and former officials from testifying; some of those people, including Taylor, have cooperated anyway, following subpoenas compelling their testimony before the House.

Taylor emerged as a major figure in the probe after Kurt Volker, former U.S. special envoy to Ukraine, provided copies of text messages to Congress as part of his cooperation with the investigation.

One key exchange on Sept. 9 shows Taylor texting Sondland, writing, "I think it's crazy to withhold security assistance for help with a political campaign."

Sondland responded: "Bill, I believe you are incorrect about President Trump's intentions. The President has been crystal clear no quid pro quo's of any kind. The President is trying to evaluate whether Ukraine is truly going to adopt the transparency and reforms that President Zelensky promised during his campaign."

Taylor states in his written remarks that "I still believe that" withholding the aid contingent upon political probes is "crazy."

Sondland said in his own opening statement last week that Trump had directed him and others to work with Giuliani - who is not a formal member of the Trump administration - to push Ukraine toward the investigations being sought.

Taylor, who had previously served as U.S. ambassador to Ukraine during the Bush administration, had traveled to Kyiv in June, after agreeing to serve as a diplomat under Trump. There he found an "irregular, informal channel of U.S. policy-making" that included Giuliani, according to the opening statement.

Taylor says he and others "sat in astonishment" after hearing in a July 18 video conference call with an Office of Management and Budget official that the Ukraine aid was being held up without a clear explanation.

The very next day, Taylor says he heard that Sondland had connected an Oval Office meeting for Zelensky with "investigations" - a link that "so irritated Ambassador [John] Bolton that he abruptly ended the meeting." Bolton was concerned that a call between Trump and Zelensky "would be a disaster," Taylor wrote.

- CNBC's Jacob Pramuk contributed to this report.
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