Southwest Airlines Co.’s dedication to an all-737 fleet entered a new phase Sunday as the carrier closed out deliveries of one generation of the jet and turned attention to the next.

From now on, the airline will receive only 737 Max planes, the latest iteration of the narrow-body aircraft that is Boeing Co.’s largest source of profit. Southwest operates the biggest 737 fleet.

Southwest first ordered 63 of Boeing’s 737-700s in 1993, serving as the launch customer for the so-called Next Generation model and helping Boeing “move forward with the development of the -700 and -800 programs,” Chief Executive Officer Gary Kelly said. It received the first of the aircraft in December 1997, and now operates 512 of the -700s and 202 -800s.

“We’ll continue to fly these airplanes for many, many years to come,” Kelly told employees in a regularly recorded message Monday. But in some ways, he said, the transition marks “the end of an era for this workhorse airplane.’’

Southwest is already flying about 16 Max 8s, according to the Dallas-based carrier’s website, and has 237 Max of that model on order in addition to 30 Max 7 aircraft. The first Max 7 will arrive next year.