But moving too quickly toward drafting articles of impeachment could expose Democrats to charges that their inquiry was a rush to tarnish the Trump presidency rather than a pursuit of the truth.

Mr. Trump and other top administration officials, as well as his personal lawyer Rudolph W. Giuliani, embarked in recent months on a campaign to pressure President Volodymyr Zelensky of Ukraine to open investigations that could benefit Mr. Trump politically. A whistle-blower complaint helped bring the scandal more fully into public view and prompted the impeachment inquiry, and Democrats say they want to ensure that they are fully scrutinizing the facts before they move forward.

“There is another risk, which is you don’t get to the bottom of the story,” Mr. Himes said. “Was Rudy Giuliani running his own State Department? What other people were pressured to go along with this?”

The White House’s charged assertion late Tuesday that it would try to stymie the inquiry came in a letter from Pat A. Cipollone, the White House counsel, but the document read more like a political argument than a legal one.

“Put simply, you seek to overturn the results of the 2016 election and deprive the American people of the president they have freely chosen,” Mr. Cipollone wrote. “Many Democrats now apparently view impeachment not only as a means to undo the democratic results of the last election, but as a strategy to influence the next election, which is barely more than a year away.”

[As the White House counsel, Mr. Cipollone is building a case for defiance on impeachment.]

Mr. Trump said on Wednesday that he was ready for a long fight with the Democrats but implied that he might reconsider if the House were to hold a vote authorizing the inquiry and granting Republicans and the White House new powers to call and cross-examine witnesses in the inquiry.

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“We would if they give us our rights,” he said of Democrats.

And Mr. Trump’s congressional allies continued to try to undercut the impeachment case. Senator Lindsey Graham, Republican of South Carolina and the chairman of the Senate Judiciary Committee, said he would invite Kurt D. Volker, the former United States special envoy to Ukraine, to testify in public if the House did not release of a transcript of its private interview with him.