The resolution itself under consideration on Thursday defines four authorities for the inquiry.
It would allow Mr. Nadler to designate any hearing of the full Judiciary Committee or its subcommittees as part of the investigation, a measure Democrats believe could help expedite their work by spreading it across the smaller, nimbler panels.
Under the new procedures, staff attorneys would be afforded time at each hearing to directly question witnesses. Democratic and Republican lawyers would each be given 30-minute blocks after lawmakers had exhausted their own questioning time.
The resolution also includes rules for how information collected by the committee — including classified material and grand jury secrets — will be handled. Most information will be treated as private by default, unless the chairman designates otherwise.
And for the first time, the committee’s vote would grant Mr. Trump and his legal team formal due process, by allowing his lawyers to respond to committee proceedings in writing in real time.
“No matter how we may disagree with him, President Trump is entitled to respond to the evidence in this way,” Mr. Nadler said.
But Republicans pointed out that the language falls well short of the privileges extended to the president’s legal teams in impeachment inquiries of President Richard Nixon and President Bill Clinton, where the defense was allowed to participate in all committee hearings, cross-examine witnesses and recommend witnesses for hearings.
“Not allowing the president’s counsel the same kind of rights as was done in the two previous presidential impeachments that have been put before this committee is a gross denial of due process,” said Representative Jim Sensenbrenner, Republican of Wisconsin and a former chairman of the Judiciary panel. “We are the committee that is supposed to stand up and protect the constitutional rights of everybody.”
The committee plans to put the new rules to use on Sept. 17, when Corey Lewandowski, Mr. Trump’s former campaign manager and an important witness to the special counsel’s obstruction of justice investigation, is scheduled to appear before the committee. Mr. Lewandowski was told to appear under subpoena and has indicated his willingness to come, but the White House could still try to intervene, preventing his testimony like those of past witnesses.