Mr. Trump never pursued it, but the F.B.I. building continued to intersect with his business — and later with his presidency. As recently as early 2015, months before he announced his candidacy, an executive at his company expressed concern to a congressional aide about the redevelopment project creating potential competition for Mr. Trump’s hotel. And now, as the first real estate developer turned president, Mr. Trump has again taken an interest in the F.B.I. project.

Within months of his taking office, his administration killed the original plan to trade the Hoover site for a suburban campus. A little over a year into Mr. Trump’s term, and after at least one meeting in which the president was personally involved, the administration announced a new plan that would keep the F.B.I. on the existing site in a new building, rather than turn over the property for commercial development.

It is not clear that putting another commercial development on Pennsylvania Avenue, even one with a competing hotel, would necessarily hurt Mr. Trump’s hotel. Still, the degree to which Mr. Trump influenced decisions about the F.B.I. building has emerged as another flashpoint in the running debate over whether his business holdings create conflicts of interest with his duties as president.

The sudden change in plans for the F.B.I. project has already prompted an inspector general’s report that documented the president’s involvement in the process. And as Democrats make plans to investigate Mr. Trump more aggressively should they win control of the House in the midterm elections next month, they are zeroing in on the issue as one of their priorities and saying that the president should have recused himself entirely from any decisions about the building.

As an initial step, Representative Elijah E. Cummings of Maryland, the top Democrat on the House Oversight Committee, and four other House Democrats sent a letter to the General Services Administration on Thursday seeking a trove of documents about the F.B.I. project.