WASHINGTON — The death of Representative Elijah E. Cummings of Maryland on Thursday left a gaping void at the helm of a crucial investigative committee leading the impeachment inquiry into President Trump, setting off a quiet but consequential contest among Democrats to succeed him as chairman of the House Oversight and Reform Committee.

Democrats said that Representative Carolyn B. Maloney of New York, now the senior Democrat on the panel, would serve as the acting chairwoman, in line with House rules, and that a permanent leader would be elected at a later time.

That puts Ms. Maloney, 73, a 14-term congresswoman who represents New York City, in a critical position, as impeachment investigators delve deeper into their inquiry, calling witnesses across the Trump administration and inside the White House and issuing subpoenas and document requests to learn more about the president’s dealings with Ukraine.

Mr. Cummings was an exceptionally active chairman even as he grew ill; in the final week of his life, he spoke daily, cellphone to cellphone, with Speaker Nancy Pelosi to discuss the status of the impeachment inquiry and court cases related to other investigations of Mr. Trump and his administration.