Republicans dismissed that as partisan wishful thinking. In the end, they argued, Mr. Sondland was at least as damaging to the Democrats’ case as he was helpful to it. Other officials like Vice President Mike Pence and Energy Secretary Rick Perry rushed out statements through aides disputing portions of his testimony.

“They have yet to point to a shred of evidence when it comes to impeachable offenses,” Representative Elise Stefanik, Republican of New York, told reporters outside the hearing room. Asked the most important piece of exculpatory evidence that lawmakers had heard, she said, “the president’s own words.”

In some ways, Mr. Sondland’s testimony reoriented the debate. He noted that when it came to a quid pro quo, there were two separate questions — whether a White House meeting coveted by President Voldymyr Zelensky of Ukraine was conditioned on his willingness to announce that he would investigate Democrats and whether the security aid was.

Mr. Sondland confirmed text messages released weeks ago that made clear that a White House visit was certainly contingent on the investigations. No linkage with the security aid has been definitively outlined in documents released so far and other officials have testified that they did not know if the two matters were directly connected, although some thought so. Mr. Sondland said he originally did not think they were but could come up with no other explanation for the aid freeze.

He also put his finger on a distinction often overlooked: For the president, it seemed more important that Ukrainian officials announce that they were investigating Democrats than for them to actually follow through on doing it.

“I never heard, Mr. Goldman, anyone say that the investigations had to start or had to be completed,” Mr. Sondland told Daniel S. Goldman, the top Democratic counsel who questioned him. “The only thing I heard from Mr. Giuliani or otherwise was that they had to be announced in some form.”

Jill Wine-Banks, a Watergate prosecutor, said Mr. Sondland reminded her less of Mr. Dean than Jeb Magruder, a top Nixon campaign official who was convicted of perjury and spent seven months in prison. “Jeb was always sort of weaseling out of full admissions,” said Ms. Wines-Banks, who worked on Mr. Magruder’s case. “John, when he came clean, he really came clean.”