Boeing Chief Executive Dennis Muilenburg speaks during a press conference after the annual shareholders meeting at the Field Museum on April 29, 2019 in Chicago, Illinois.

Boeing's CEO Dennis Muilenburg on Monday said it is conducting simulated flights with air-safety regulators this week and plans to fly its 737 Max aircraft with the Federal Aviation Administration "very soon" to get the grounded planes cleared to return to airline service.

Aviation officials worldwide grounded the planes in mid-March in the wake of two deadly crashes of the aircraft within five months of one another. The two crashes killed a total of 346 people.

Muilenburg said he expects that the planes will get a green light to fly again by the end of the year, but declined to provide a timeline.

The Federal Aviation Administration is participating in simulated flights with Boeing this week, Muilenburg said in an an interview with CNBC's The Exchange. After that step, Boeing plans to schedule actual test flights.

Boeing has completed a software update for an anti-stall system that has been implicated in the two crashes.

Airlines that have purchased the 737 max, including American Airlines, United Airlines and Southwest Airlines have canceled thousands of flights due to the grounding and have scrambled to meet demand during the peak summer travel season.

The manufacturer will have to repair "damaged trust" of the flying public, Muilenburg said. Some airlines have said they won't charge passengers skittish about the planes to switch to flights operated with other aircraft.