Boeing Co.’s 737 MAX planes are unlikely to be ready to carry passengers again until 2020 because of the time it will take to fix flight-control software and complete other steps, an increasing number of government and industry officials say, even as the company strives to get its jet back into service this year.

The situation remains fluid, no firm timeline has been established and Boeing still has to satisfy U.S. regulators that it has answered all outstanding safety questions. But under the latest scenario, the global MAX...