President Trump on Tuesday lashed out over speculation that he was dealing with an undisclosed health issue in the aftermath of an unannounced visit to Walter Reed medical center.
Vindman testified that he felt Trump's request to investigate a political rival was "improper".
Chief Judge Beryl Howell on October 25 rejected Justice Department arguments that the House impeachment process doesn't qualify as a judicial proceeding for the purposes of turning over grand jury materials that are ordinarily kept sealed.
The House of Representatives' top lawyer told a federal court on Monday that the House is investigating whether Donald Trump lied to the special counsel Robert Mueller, and the attorney urged the judges to order the release of still-secret material from Mueller's investigation.
At the heart of the impeachment inquiry is a 25 July phone call in which Trump asked Ukrainian President Volodymyr Zelenskiy to open a corruption investigation into former US Vice President Biden and his son, Hunter Biden, and into a discredited theory that Ukraine, not Russian Federation, meddled in the 2016 US election.
Yet Vindman spent long stretches fielding Republican attacks on his loyalty to the USA and his career in public service.
Volker said he stressed that no one in the new team governing Ukraine had anything to do with the 2016 election, and that it was not credible to him that Biden would have been influenced in any way by personal or financial motivations.
Vindman said the rough transcript of the call was segregated to a small group to prevent leaks. "She also said I could do it in writing".
Vindman and Williams opened a high-stakes week of public testimony on Capitol Hill.
Kurt Volker, the former State Department envoy to Ukraine for its peace negotiations, and Tim Morrison, a former National Security Council aide.
Also scheduled to testify this week is Ambassador to the EU Gordon Sondland. Much of Sondland's private testimony to lawmakers has been contradicted by other witnesses.
Vice President Mike Pence's national security aide, Jennifer Williams, and David Holmes, a USA embassy official in Kyiv, were among those testifying behind closed doors last week, as secret depositions continue to take place alongside open hearings.
Trump's suggestion that he might himself testify in the investigation which threatens his presidency had no impact on the House Intelligence Committee's plans to interview nine witnesses this week. Trump has sought to publicly malign multiple witnesses in the inquiry, something Vindman alluded to in scathing terms on Tuesday.
Vindman was one of four officials to testify on Tuesday in the ongoing public hearings. The whistleblower is a Central Intelligence Agency official, according to people with knowledge of the matter.
"Schiff likes to claim he doesn't know who the whistleblower is..."
The U.S. Army official is an immigrant from Ukraine.
The reference to Biden and his son Hunter "struck me as political in nature".
The Democrat-led inquiry is establishing whether Mr Trump withheld aid to Ukraine in return for an inquiry into ex-Vice President Joe Biden.
"Those were the recommended talking points that were cleared through the NSC staff", he said. And he said he didn't understand there was a link between Hunter Biden and Burisma.
Vindman said the uneven power dynamic between the presidents of the East European ally and the US made the demand obvious. He said that he is grateful his father came to the United States some 40 years ago, a place "where I can live free of fear for mine and my family's safety".
Trump's 2018 and 2019 physicals were both announced ahead of time.
The hearings also include diplomats who have already testified privately that Trump and Sondland repeatedly pushed Kiev to open investigations into Democrat Joe Biden - Trump's potential 2020 reelection challenger - and withheld almost $400 million in aid and a White House meeting requested by Ukraine President Volodymyr Zelensky as pressure.
"Everyone in Ukraine is so exhausted of Burisma", Zelenskiy said, before quickly leaving the room full of reporters. Sondland told the official that US aid might be freed up if the country's top prosecutor "would go to the mike and announce that he was opening the Burisma investigation", Morrison said in previous closed-door testimony.