WASHINGTON — A crucial cache of evidence in hand, House Democrats moved quickly on Thursday with an impeachment inquiry they said would be focused tightly on President Trump’s dealings with Ukraine, using an incendiary whistle-blower complaint as a road map for their investigation.

The complaint landed like a bombshell on Capitol Hill on Thursday morning after its release by the House Intelligence Committee, and Democrats quickly seized on its narrative of allegations against Mr. Trump — chock-full of potentially damning detail, intriguing threads and characters who could become witnesses in the nascent inquiry — as an outline for their work.

After months of plodding investigating to determine whether they had grounds to impeach Mr. Trump, Democrats were working feverishly to build a case on the Ukraine matter, with some lawmakers saying they could move within a month or six weeks, possibly drafting articles of impeachment by the end of October.

“This is a cover-up,” said Speaker Nancy Pelosi, Democrat of California, who after months of resisting the move made it clear that she was determined to follow through with a formal impeachment inquiry.