WASHINGTON — The House Judiciary Committee on Thursday took its first recorded vote to press forward with a possible impeachment of President Trump, putting aside Democrats’ internal divisions for the time being in a bid to strengthen its hand in investigating whether he committed high crimes and misdemeanors.

Voting along party lines, the panel approved rules for a continuing “investigation to determine whether to recommend articles of impeachment with regard to President Donald J. Trump,” which clarified new authorities for lawmakers and laid out a process, albeit limited, for the president to respond.

Speaking after the vote, the committee’s chairman, Representative Jerrold Nadler of New York, also promised a series of hearings expanding the inquiry beyond the findings of Robert S. Mueller III, the former special counsel, to consider other potentially impeachable offenses. The first session is scheduled to take place next week with Corey Lewandowski, Mr. Trump’s former campaign manager and an important witness to the special counsel’s obstruction-of-justice investigation.

But Thursday’s action was as much a symbolic display as it was a practical exercise of constitutional powers, aimed at showing federal courts and impatient Democrats that the House is, in fact, serious about building an impeachment case, even if it is not yet taking the politically loaded step of filing charges.