FORT WORTH, Texas—A review of Boeing Co.’s 737 MAX jets has expanded to include emergency procedures used by pilots on earlier 737 models, further delaying the MAX’s return to service, according to U.S. government officials.

The Federal Aviation Administration hasn’t questioned the safety of older jets currently in service, these officials said, but the broadened review has become a significant factor in adding months to the time expected to get the grounded fleet of 737 MAX jets back in the air.

As...