George Kent, a senior State Department official in charge of Ukraine policy, told impeachment investigators that he was all but cut out of decisions regarding the country after a May meeting organized by Mick Mulvaney, the White House chief of staff, according to a lawmaker who heard the testimony.

Mr. Kent had raised concerns to colleagues early this year about pressure being directed at Ukraine by President Trump and Rudy Giuliani to pursue investigations into Mr. Trump’s political rivals.

Mr. Kent’s testimony followed a pattern that has emerged among recent witnesses. The State Department directed Mr. Kent not to appear and sought to limit his testimony, according to officials familiar with the investigation. But the House Intelligence Committee issued a last-minute subpoena, and he complied.

Tuesday was the document deadline for Vice President Mike Pence, Mr. Giuliani, the Defense Department and the Office of Management and Budget. Mr. Pence and the O.M.B. rejected the requests. A lawyer for Mr. Giuliani sent a letter to House officials saying that Mr. Giuliani would not comply with the subpoena he was issued.

How this impeachment is different

Investigators this week are calling in witnesses who aren’t typically part of the Washington news cycle: a former Russia specialist on the National Security Council, the ambassador to the European Union, a deputy assistant secretary of defense.

The range of voices puts this impeachment investigation in new historical territory, according to Philip Bobbitt, a professor at Columbia Law School and a co-author with Charles Black of “Impeachment: A Handbook.”

The Clinton impeachment had little to do with governance, Mr. Bobbit told me.

“It had nothing to do with foreign policy or defense policy,” he said. “And in Nixon’s case, there were maybe a couple of dozen people involved.”

The inquiry so far has leaned on witness depositions in addition to traditional evidentiary material like transcripts, which were a mainstay for investigators organizing the case against President Richard Nixon.