Much of the House’s investigative work is expected to focus on corroborating the whistle-blower complaint from a C.I.A. officer, which accused Mr. Trump of abusing the power of his office to pressure the Ukrainian government into investigating a leading political rival and then trying to cover it up. The depositions will most likely be conducted by committee staff and will take place out of public view to speed up the fact-finding process and avoid the political implications of public hearing.

The subpoena for documents is far-reaching and mirrors early voluntary requests sent to the State Department and the White House. It demands a full transcript of the July call between Mr. Trump and Mr. Zelensky, a list of any State Department officials who listened to or received a readout of the call, and any records created by the department in relation to it. It also seeks any files related to efforts by the president’s personal lawyer, Rudolph W. Giuliani, to push investigations into Mr. Biden or other matters involving Ukraine; and it calls for records related to the Trump administration’s decision to temporarily withhold $391 million in security aid from Ukraine.

Mr. Pompeo was given one week to produce the material.

Democrats presented their deposition requests as nonnegotiable, listing dates for early October appearances by officials who were either mentioned in a whistle-blower complaint released this week or are connected to American policy work in the region. They include Marie L. Yovanovitch, the former American ambassador to Ukraine; Kurt D. Volker, the United States special envoy to Ukraine; George Kent, a deputy assistant secretary of state for European and Eurasian affairs; T. Ulrich Brechbuhl, a State Department counselor; and Gordon Sondland, the ambassador to the European Union.

Mr. Volker abruptly resigned on Friday.

“The committees are investigating the extent to which President Trump jeopardized national security by pressing Ukraine to interfere with our 2020 election and by withholding security assistance provided by Congress to help Ukraine counter Russian aggression,” said the letters, sent to Mr. Pompeo by Representative Eliot L. Engel of New York, the chairman of the Foreign Affairs Committee; Mr. Schiff of the Intelligence Committee; and Representative Elijah E. Cummings of Maryland, the chairman of the Oversight and Reform Committee.

[Read the letter from three House committee chairmen informing Secretary of State Mike Pompeo about the subpoena.]

After months of stonewalling congressional oversight requests sent by the House largely with impunity, the Trump administration now faces a crucial choice: cooperate and potentially hand over witnesses and documentary evidence that could help Democrats build a case against Mr. Trump, or refuse, and risk bolstering a possible impeachment article charging the president with obstructing Congress.

Other investigative actions were underway, too. The Intelligence Committee continued to negotiate to meet with the whistle-blower in a secure setting to try to identify other officials who witnessed the alleged events and who would be willing to cooperate with their work.