WASHINGTON — House impeachment investigators widened the reach of their inquiry on Friday, subpoenaing the White House for a vast trove of documents and requesting more from Vice President Mike Pence to better understand President Trump’s attempts to pressure Ukraine to investigate his political rivals.

The subpoena, addressed to Mick Mulvaney, the acting White House chief of staff, calls for documents and communications that are highly delicate and would typically be subject in almost any White House to claims of executive privilege. If handed over by the Oct. 18 deadline, the records could provide keys to understanding what transpired between the two countries and what steps, if any, the White House has taken to cover it up.

The request for records from a sitting vice president is unusual in its own right, and Mr. Pence’s office quickly signaled he may not comply. In a letter to Mr. Pence, the chairmen of three House committees conducting the impeachment inquiry wrote that they were interested in “any role you may have played” in conveying Mr. Trump’s views to Ukraine. They asked for a lengthy list of documents detailing the administration’s dealings with Ukraine, to be produced by Oct. 15.

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The actions came at the end of another day of fast-moving developments in the House impeachment investigation, which is centered on allegations that Mr. Trump and his administration worked to bend America’s diplomatic apparatus for his own political benefit.

Mr. Trump himself appeared resigned to the prospect that he would be impeached, and was gearing up for an epic political battle to defend himself, predicting the Democrat-led House would approve articles of impeachment against him and the Republican-controlled Senate would acquit him.

“They’ll just get their people,” he said of House Democrats. “They’re all in line. Because even though many of them don’t want to vote, they have no choice. They have to follow their leadership. And then we’ll get it to the Senate, and we’re going to win.”

Privately, Mr. Trump briefly joined a conference call of House Republicans, defending his interactions with Ukraine and rallying his party to fight for him.

On Capitol Hill, the impeachment investigation continued gaining steam, as requests and information from witnesses began to stack up. For more than six hours on Friday, the House Intelligence Committee questioned the intelligence community’s independent watchdog who first fielded a whistle-blower complaint that has spurred the formal impeachment inquiry into Mr. Trump. Michael Atkinson, the intelligence community inspector general, had received the complaint and explained his own preliminary investigation into its validity before seeking to deliver it to Congress.

“What the inspector general said last time was, the whistle-blower pulled the fire alarm,” Representative Mike Quigley, Democrat of Illinois, told reporters. “We have now seen the smoke and the fire.”

How the White House, which has routinely rejected congressional requests for information, responds to the demands for documents could significantly shape the impeachment investigation going forward. Under normal circumstances, the White House could claim materials referred to in both requests were privileged, using that as a defense in court.

Press secretaries for the White House and the vice president issued similar statements assailing the demands, but did not clearly indicate whether they would comply or not. Stephanie Grisham, the White House press secretary, said the subpoena “changes nothing” and called it “just more document requests, wasted time and taxpayer dollars that will ultimately show the president did nothing wrong.”

Katie Waldman, Mr. Pence’s press secretary, promptly said that “given the scope, it does not appear to be a serious request but just another attempt by the ‘Do Nothing Democrats’ to call attention to their partisan impeachment.”

But that will not help Mr. Trump’s case on Capitol Hill. Speaker Nancy Pelosi and the chairmen leading the inquiry have consistently warned the White House that noncompliance with their requests will be viewed as obstruction of Congress, itself a potentially impeachable offense.

“The White House has refused to engage with — or even respond to — multiple requests for documents from our Committees on a voluntary basis,” said the letter to Mr. Mulvaney, signed by Representative Adam B. Schiff of California, the Intelligence Committee chairman; Representative Eliot L. Engel of New York, the Foreign Affairs Committee chairman; and Representative Elijah E. Cummings of Maryland, the Oversight and Reform Committee chairman. “After nearly a month of stonewalling, it appears clear that the president has chosen the path of defiance, obstruction, and cover-up.”

In addition to the new subpoena and request, a significant subpoena deadline for the State Department to hand over similar material in its possession was also scheduled to arrive by the end of the day. It was not immediately clear if the department had complied or not.

Even as they worked, lawmakers from both parties continued Friday morning to try to make sense of a tranche of texts between American diplomats and a top aide to the Ukrainian president. Those messages were released late Thursday night, and called into question the truthfulness of Mr. Trump’s claim that there had been no quid pro quo attached to his pressing Ukraine to investigate former Vice President Joseph R. Biden Jr., his son and other Democrats.

The House committees are scheduled to interview additional witnesses implicated in the texts next week. Gordon D. Sondland, the ambassador to the European Union and a Trump supporter who been actively involved in diplomacy with Ukraine, is expected to appear on Tuesday, and Marie L. Yovanovitch, the former American ambassador to Ukraine, on Friday.

Democrats have pounced on the texts as further evidence that Mr. Trump was treating the investigations as a precondition to giving Ukraine, an American ally that borders Russia, a meeting with the president and a $391 million package of security aid. Most Republicans remained silent or stood by Mr. Trump in light of the new messages, but a few raised alarms.

Senator Mitt Romney, Republican of Utah, one of the few members of Mr. Trump’s party who have been critical of the conduct at the center of the impeachment inquiry, issued a statement condemning the president’s public comments on Thursday in which he invited China as well as Ukraine to investigate the Bidens.

“When the only American citizen President Trump singles out for China’s investigation is his political opponent in the midst of the Democratic nomination process, it strains credulity to suggest that it is anything other than politically motivated,” Mr. Romney said. “By all appearances, the president’s brazen and unprecedented appeal to China and to Ukraine to investigate Joe Biden is wrong and appalling.”

Democrats on Capitol Hill said Mr. Atkinson’s account reinforced the seriousness of their effort.

A Trump appointee, Mr. Atkinson helped set off the current saga less than a month ago when he notified Congress’s intelligence committees that he had received an anonymous whistle-blower complaint that he deemed to be “urgent” and credible. The acting director of national intelligence intervened initially to block Mr. Atkinson from sharing the complaint with Congress, but ultimately the Trump administration relented and allowed its public release.

In the complaint, the whistle-blower wrote that multiple government officials had provided him information that “the President of the United States is using the power of his office to solicit interference from a foreign country in the 2020 U.S. election.”

Specifically, he said that Mr. Trump and his personal lawyer, Rudolph W. Giuliani, had pressed Ukraine to conduct the investigations, potentially using the prospect of a meeting that the new Ukrainian president badly wanted with Mr. Trump and withholding the aid earmarked for the country as leverage to secure the investigations. The White House tried to cover up aspects of the events, the complaint said.

Mr. Atkinson has already appeared once before the House Intelligence Committee, but he was barred then from speaking in detail about the complaint. On Friday, Mr. Atkinson walked lawmakers through the complaint and some of the steps he took to try to evaluate the veracity of his claims, including showing documents. The inspector general declined to share with the committee names of officials he spoke during his brief investigation, according to one person familiar with his testimony.

Details of the complaint, including a July call between Mr. Trump and President Volodymyr Zelensky of Ukraine, have already been verified. The texts released late Thursday also appeared to comport with elements of the complaint.

Maggie Haberman contributed reporting from New York, and Annie Karni from Washington.