WASHINGTON — After months of conceding to demands from a small group of House Republicans for more visibility into continuing investigations, the deputy attorney general, Rod J. Rosenstein, pushed back on Tuesday, declaring that the Justice Department “is not going to be extorted.”

His comment came the day after revelations that several of those Republicans, led by Representative Mark Meadows of North Carolina and other loyalists of President Trump, had drafted articles of impeachment to use against Mr. Rosenstein in case the long-simmering dispute with the deputy attorney general boiled over.

Though their conflict is ostensibly over the Justice Department’s production of sensitive documents to Congress, Democrats believe that the bureaucratic disagreement belies a more fundamental concern for the lawmakers: protecting Mr. Trump from the special counsel investigation, which Mr. Rosenstein oversees.

Mr. Rosenstein said he had been threatened, though he did not name the Republicans.

“There have been people who have been making threats, privately and publicly, against me for quite some time,” he said. “And I think they should understand by now, the Department of Justice is not going to be extorted.”