Democrats continued their whirlwind investigation of Donald Trump on Tuesday as another witness testified before Congress, building momentum towards a likely impeachment of the president.

Trump sought to fight back by drawing attention to a TV interview in which Hunter Biden, the son of the former vice-president Joe Biden, acknowledged “poor judgment” in his business dealings in Ukraine but denied any wrongdoing.

George Kent, the deputy assistant secretary of state, became the latest official to appear in private before three House committees. In emails supplied to Congress by the state department inspector general, Kent expressed concerns about White House efforts to remove the then ambassador to Ukraine.

The impeachment inquiry is moving at dizzying speed. The Axios website noted that if everyone agrees to appear, Democrats will have interviewed 11 administration officials by the end of next week. Every witness has “bolstered the case against Trump”, Axios added, leaving White House officials demoralised or panicked.

In a press conference on Tuesday evening, the House intelligence committee chair, Adam Schiff, said House Democrats had “made dramatic progress in answering some of the questions surrounding that July telephone call” between Donald Trump and the Ukrainian president, Volodymyr Zelenskiy. Pelosi said the House was on a “path to truth” but said a full vote to authorize the inquiry was not yet necessary, despite White House criticism.

“There is no requirement that we have a vote. We will not be having a vote,” she said.

“We are on the path of fairness,” she continued. “We are not here to call bluffs. We are on a path that is taking us to a path to truth, a timetable that respects our constitution.”

The hearings have been held behind closed doors but Democrats may yet decide to publish transcripts. Trump, who has been leading his own defence, tweeted on Tuesday: “Democrats are allowing no transparency at the Witch Hunt hearings. If Republicans ever did this they would be excoriated by the Fake News. Let the facts come out from the charade of people, most of whom I do not know, they are interviewing for nine hours each, not selective leaks.”

I am not part of whatever drug deal Rudy and Mulvaney are cooking up … Giuliani’s a hand grenade John Bolton

The torrent of damaging revelations continued on Monday when Fiona Hill, a British-born former senior director for Europe and Russia on the White House National Security Council (NSC), spoke to the House committees for 10 hours.

According to the New York Times and the Wall Street Journal, Hill described a sharp exchange on 10 July between the then national security adviser, John Bolton, and the US ambassador to the European Union, Gordon Sondland. It concerned the role played by Rudy Giuliani, the former New York mayor commonly described as Trump’s lawyer, in trying to persuade the Ukrainian government to open investigations into Democrats including Biden.

Hill said Bolton instructed her to tell the NSC’s attorney that Giuliani was acting in concert with White House chief of staff, Mick Mulvaney, in a rogue operation with legal implications.

“I am not part of whatever drug deal Rudy and Mulvaney are cooking up,” Bolton instructed Hill to tell the NSC lawyer, according to her testimony.

The House intelligence committee chairman, Adam Schiff, arrives for a closed door meeting on Capitol Hill in Washington on Tuesday. Photograph: Manuel Balce Ceneta/AP

She said Bolton had told her on an earlier occasion: “Giuliani’s a hand grenade who’s going to blow everybody up.”

Q&A How do you impeach the US president? Show Article 1 of the United States constitution gives the House of Representatives the sole power to initiate impeachment and the Senate the sole power to try impeachments of the president. A president can be impeached if they are judged to have committed "treason, bribery, or other high crimes and misdemeanors" – although the US Constitution does not specify what “high crimes and misdemeanors” are.

The formal process starts with the House of Representatives passing articles of impeachment, the equivalent of congressional charges. According to arcane Senate rules, after the House notifies the Senate that impeachment managers have been selected, the secretary of the Senate, Julie Adams, tells the House that the Senate is ready to receive the articles. Then impeachment managers appear before the Senate to “exhibit” the articles, and the Senate confirms it will consider the case. The presiding officer of the Senate notifies the supreme court chief justice, John Roberts, of the impending trial. Roberts arrives in the Senate to administer an oath to members. The presiding officer will then administer this oath to senators: “I solemnly swear that in all things appertaining to the trial of the impeachment of Donald Trump, now pending, I will do impartial justice according to the constitution and laws, so help me God.” The Senate must vote on a resolution laying out ground rules for the trial including who the key players will be, how long they will get to present their cases and other matters. After the Senate is “organized”, the rules decree, “a writ of summons shall issue to the person impeached, reciting said articles, and notifying him to appear before the Senate upon a day and at a place to be fixed by the Senate”. A president has never appeared at his own impeachment trial. Trump will be represented by the White House counsel, Pat Cipollone, and his personal lawyer Jay Sekulow, among others. After the oath, the trial proper will begin. Senators may not speak during the proceedings but may submit written questions. The question of witnesses and other matters would be decided on the fly by majority vote. A time limit for the proceedings will be established in the initial Senate vote. The senators will then deliberate on the case. In the past this has happened behind closed doors and out of public view. The senators vote separately on the two articles of impeachment – the first charging Trump with abuse of power, the second charging him with obstruction of Congress. A two-thirds majority of present senators – 67 ayes if everyone votes – on either article would be enough to convict Trump and remove him from office. But that would require about 20 Republicans defections and is unlikely. The more likely outcome is a Trump acquittal, at which point the process is concluded. Two presidents have previously been impeached, Bill Clinton in 1998, and Andrew Johnson in 1868, though neither was removed from office as a result. Richard Nixon resigned in 1974 before there was a formal vote to impeach him. Tom McCarthy in New York

Hill also testified on Monday about Trump’s decision, taken despite strenuous objections from aides including herself, to recall the ambassador to Ukraine, Marie Yovanovitch.

The Washington Post reported that Hill had confronted Sondland over Giuliani’s activities, which were not coordinated with officials charged with carrying out foreign policy. Sondland is due to give his version of events on Thursday.

I did nothing wrong at all, but it was poor judgment to be in the middle of something that is … a swamp in many ways Hunter Biden

The impeachment inquiry was sparked by a whistleblower complaint filed in August that in part described a 25 July phone call between Trump and the Ukrainian president, Volodymyr Zelenskiy, in which Trump requested the “favor” of an investigation into Biden, a potential rival in the 2020 election.

Trump and Republicans have repeated unproven allegations of corruption against Hunter Biden, who was on the board of a gas company in Ukraine while his father was involved in international efforts to curb corruption in its government.

Breaking his silence over his business dealings in Ukraine and China, the younger Biden told ABC News on Tuesday he had allowed himself to become involved in what he described as “a swamp”. But he repeatedly denied ever discussing his foreign work with his father.

“In retrospect, I think there was poor judgment on my part,” he said. “I know I did nothing wrong at all, but it was poor judgment to be in the middle of something that is … a swamp in many ways.”

Several Democratic strategists have questioned the wisdom of Hunter Biden speaking out. The fear is that it might switch the focus away from Trump’s efforts to enlist the help of the Ukraine government and on to the president’s home ground: his unsubstantiated claims of corruption on the part of the Bidens.

The week could deteriorate rapidly for Trump, whose effort to rally defenders in his own party has been damaged by concerns about a growing disaster in northern Syria, following Trump’s abrupt pullback there, and a sense that major secrets attached to the Ukraine scandal are yet to emerge.

Meanwhile, on Tuesday afternoon, Giuliani formally notified the House that he wouldn’t submit documents demanded via subpoena by the Trump-Ukraine impeachment inquiry.

In a letter to the relevant committee chairmen from his erstwhile lawyer, Jon Sale, the inquiry was condemned as “an unconstitutional, baseless and illegitimate ‘impeachment inquiry’” and the subpoena called “overbroad and unduly burdensome”.

The government budget office said that it would not comply with the demand for documents, either.

The subpoena issued to the office of management and budget related to the delay in military funds to Ukraine.

That issue is at the heart of the impeachment inquiry, in relation to allegations that Trump held back congressionally approved aid to Ukraine as a form of pressure to persuade the new president, Volodymyr Zelenskiy, to investigate the Bidens.

Giuliani is also facing scrutiny over his dealings involving Turkey. On Tuesday the Washington Post reported that he had privately urged Trump to extradite Fethullah Gülen, the US-based Muslim cleric accused by Turkey of instigating a failed 2016 coup. It remains unclear why Giuliani would have pushed the issue, which is of great importance to the Turkish president, Recep Tayyip Erdoğan, according to the Post.

Vivian Ho contributed reporting