WASHINGTON — Speaker Nancy Pelosi announced a formal impeachment inquiry on Tuesday amid mounting furor over President Trump’s efforts to pressure Ukraine’s government to investigate former Vice President Joseph R. Biden Jr., apparently the subject of a classified whistle-blower complaint the administration refused for weeks to show to Congress before dropping objections.

Mr. Trump, meanwhile, said he planned on Wednesday to release the transcript of a phone call he had in July with President Volodymyr Zelensky of Ukraine. Mr. Trump insisted it would show that he said nothing inappropriate, but scrutiny about his conduct toward Ukraine has spread beyond the single conversation.

Here are some of the basic facts behind the controversy.

Mr. Trump is said to have pressured Mr. Zelensky to investigate Mr. Biden and his younger son, Hunter — both directly and through a proxy, Rudolph W. Giuliani, one of Mr. Trump’s personal lawyers. As a leading candidate to be the Democratic Party’s 2020 presidential nominee, Mr. Biden is Mr. Trump’s political rival.

As vice president, Mr. Biden pushed the Ukrainian government in 2015 to fire its top prosecutor, Viktor Shokin, who was widely seen as an obstacle to reform because he failed to bring corruption cases. At the time, Mr. Biden’s son sat on the board of a Ukrainian energy company, Burisma Holdings.

Mr. Trump and his allies have insinuated, without evidence, that Mr. Biden was trying to protect the company from prosecution. An investigation into him, even if it were unfounded or turned up no evidence of a crime, could damage his campaign prospects by suggesting wrongdoing.

This is the big question. The White House froze more than $391 million in military assistance to Ukraine this summer that Congress had appropriated. The money was intended to help Ukraine defend itself from Russian territorial aggression, including a military conflict in eastern Ukraine that has killed more than 13,000 people since 2014.

Mr. Trump has given conflicting explanations for the freeze. On Monday, he cited corruption in Ukraine as the reason for the delay. On Tuesday, he instead said he had held up the military assistance because European countries had not paid their fair share to help defend Ukraine, a former Soviet republic, from Russian incursions.

Mr. Trump directed Mick Mulvaney, the acting White House chief of staff, to pause the aid in the days before his July phone call with Mr. Zelensky, senior administration officials said. The Trump administration abruptly unfroze the package this month amid mounting questions about what Mr. Trump was doing with Ukraine.

An intelligence official filed a whistle-blower complaint last month about the president’s actions. The inspector general for the intelligence community deemed the complaint “credible” and “urgent” and forwarded it to the acting director of national intelligence, Joseph Maguire, under a law that says such complaints must be shown to Congress within a week.

But Mr. Maguire refused to share the complaint with Congress, saying the Justice Department disagreed with the inspector general’s conclusion that its subject matter was covered under the law that requires disclosing such complaints to Congress. The issue came into the open when the House Intelligence Committee chairman, Representative Adam B. Schiff, Democrat of California, sent an angry letter to Mr. Maguire on Sept. 10, accusing him of violating the law.

Mr. Maguire relented as the impeachment inquiry came into focus. He was expected to release a redacted version of the complaint in coming days, people familiar with the situation said late on Tuesday. Administration officials were also said to be working on a deal to allow the whistle-blower to file the complaint to congressional investigators.

Mr. Maguire is set to testify about the matter on Thursday.

The complaint’s full details remain a mystery, as does the whistle-blower’s identity. Because Mr. Trump and Mr. Giuliani have openly acknowledged pressuring Ukraine about “corruption” and the Bidens, it is not clear how much the complaint involves that is not already in plain view.

But in a closed-door briefing with the House Intelligence Committee, the inspector general for the intelligence community, Michael Atkinson, said that the complaint involved multiple actions, according to two officials familiar with his briefing, suggesting that the matter goes beyond Mr. Trump’s July phone call.

The president insists that he has been unfairly accused, saying — without offering evidence — that the whistle-blower is “partisan” and that Democrats and the news media are initiating a new “witch hunt” against him. Mr. Trump has also said that he is aware that his conversations with foreign leaders are monitored by numerous government officials and that he would not incriminate himself so easily.

Mr. Giuliani has communicated with Ukrainian officials for months about the Bidens. He has also pressed them about the circumstances of the 2016 disclosures of payments earmarked by a Russia-aligned Ukrainian political party to Paul Manafort, Mr. Trump’s 2016 campaign chairman, who is in federal prison on convictions related to his Ukrainian political work. Mr. Giuliani has sought information about both subjects and traveled to Madrid this summer for a meeting with one of Mr. Zelensky’s top aides, whom he urged to investigate the matters.

In May, Mr. Giuliani told The New York Times that he was pushing Ukraine to investigate the Bidens “because that information will be very, very helpful to my client, and may turn out to be helpful to my government.”

No evidence has emerged that Mr. Biden was trying to help his son when he pushed for the dismissal of the Ukrainian prosecutor, who was widely seen in the West as corrupt. Stamping out high-level corruption in Ukraine had long been a central goal of Obama administration policy toward the country and a standard condition for Western aid. On Saturday, Mr. Biden said he had never spoken with his son about any overseas work.

Mr. Biden played a lead role in the Obama administration’s diplomacy with Kiev, though administration officials worried that his son’s work for the energy company, Burisma Holdings, could create at least the perception of a conflict of interest.

But Ukraine’s current top prosecutor has said there is no evidence of wrongdoing by the Bidens to investigate.

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