WASHINGTON—President Donald Trump’s nominee to lead the Justice Department’s antitrust efforts is facing an extended limbo in the Senate, prolonging uncertainty for potential mergers, including AT&T Inc.’s bid to acquire Time Warner Inc.

The delay in Makan Delrahim’s nomination is due in part to objections raised by Sen. Elizabeth Warren (D., Mass.), a leading figure in the Democrats’ liberal wing who has been a vocal critic of large corporate mergers that she says could hurt consumers, according to people familiar with...