US airlines using the Boeing 737 MAX aircraft will conduct demonstration flights with company officials on board as part of an effort to convince customers the plane is safe.

American, United and Southwest airlines will make the flights as part of a public relations campaign to rebuild confidence in the MAX after crashes in Indonesia and Ethiopia killed a total of 346 passengers and crew. The airlines haven't yet set a date for the flights.

The flights are a variation on a theme struck by Boeing CEO Dennis Muilenburg and Federal Aviation Administration (FAA) Administrator Stephen Dickson. Muilenburg said the company has conducted 500 test flights. He was on board for at least two and said other Boeing employees were "eager to do the same'.

Dickson, a former Air Force pilot and executive at Delta Airlines, said he would test the MAX's new flight control software by climbing into a flight simulator. The FAA has been criticized for lax oversight in its approval of Boeing's top-selling plane.

MAX jets were grounded in March following crashes on Oct 29, 2018, of a Lion Air flight in Indonesia and March 30 of an Ethiopian Airlines flight in Africa. Investigators have focused on the MAX's automated anti-stall system called the Maneuvering Characteristics Augmentation System (MCAS) that may have erroneously pointed the nose of the plane down to gain speed to avoid a midair stall and into a fatal plunge. China was the first to ground the planes, and the US was the last.

Boeing's software update hasn't yet been approved by the FAA, and it's unclear what additional pilot training will be required before approving the MAX's return to commercial service. European and other regulators may impose different requirements at different times that could lead to a staggered return of the jet to service.

"It's really important for our customers to see the plane is flying again," Ross Feinstein, a spokesman for American Airlines Group, told The Wall Street Journal.

Other top executives, members of the media and possibly corporate clients may board the early flights, the newspaper said.

WestJet, a Canadian carrier, said its market research found that 59 percent of Canadian fliers are uncomfortable flying on a MAX.

American and United have scratched the Boeing MAX from their schedules until January, and Southwest doesn't expect the plane to return to service until February.

The union representing flight attendants for American Airlines said its 28,000 members "refuse to walk on a plane that may not be safe".

In a letter issued in response to Muilenburg's congressional testimony, the union said his testimony showed "there were serious breakdowns in the supervision of the 737 MAX'.

"It is important to recognize that many questions and the fear of working on this aircraft is an ongoing conversation," Lori Bassani, president of the Association of Professional Flight Attendants, said in a statement. "Our workforce should not and will not come to work afraid for their safety."

Meanwhile, Ryanair, Europe's biggest budget carrier, said it doesn't expect to fly the MAX before summer. In July, Ryanair said it would rename the MAX the "8200".