Boeing Co.’s woes escalated as European aviation regulators joined Asian and Latin American authorities in grounding the 737 MAX jet, and lawmakers on Capitol Hill urged U.S. airlines to voluntarily park those planes after two deadly crashes of the aircraft in the past five months.

The crashes have raised questions about the plane’s flight-control system. The Wall Street Journal reported Tuesday that in response to the first crash in October, Boeing is making a significant change to the software that controls a stall-prevention...