WASHINGTON — The House Judiciary Committee on Monday subpoenaed the former top White House aide Rob Porter to testify about President Trump’s efforts to impede the Russia investigation and asked a court to expedite a ruling on whether Donald F. McGahn II, the former White House counsel, must testify, pushing forward in its expansive inquiry into whether to impeach Mr. Trump.

The moves are the latest intensification of a multipronged effort by the Democrat-led House to explore Mr. Trump’s conduct in office with an eye toward determining if he obstructed justice and committed impeachable offenses. They unfolded as a growing chorus of Democratic lawmakers have come out over the past several weeks in favor of impeachment, and as the party’s progressive base clamors for more aggressive action in the face of insistence by Speaker Nancy Pelosi that the move is premature.

Mr. Porter was a key witness to Mr. Trump’s repeated attempts to thwart the special counsel’s investigation, including the president’s efforts to get Mr. McGahn to falsely deny a New York Times article that revealed his order to fire the special counsel, Robert S. Mueller III.

The Judiciary Committee went to court this month to enforce its subpoena of Mr. McGahn after the Trump administration asserted that top presidential aides were “absolutely immune” from its subpoenas. In its legal filing on Monday, lawyers for the House argued that the former White House counsel was the “most critical fact witness” in the committee’s examination of whether the president obstructed justice, including when he instructed Mr. McGahn to remove Mr. Mueller and then to lie about whether the president had done so, and later, to issue a statement lying publicly about it.