An aerial photo shows several Boeing 737 MAX airplanes grounded at Boeing Field in Seattle, Washington, U.S. March 21, 2019.

The meeting attendees included Mike Sinnett, a Boeing vice president; Craig Bomben, a top Boeing test pilot; and senior lobbyist John Moloney. The meeting was first reported by The Dallas Morning News.

Pilots asked Boeing at a private meeting in November to take emergency action that would have likely grounded the Max, but Boeing officials resisted, according to an audio recording of the meeting reviewed by CNBC.

Weeks after the first of two 737 Max crashes, American Airlines pilots angrily pushed Boeing to fix the anti-stall software suspected in the deadly disasters.

Sinnett told the pilots at the meeting that the company was working on a software fix that would be ready in as little as six weeks, and it would not rush the process. He also said it was unclear whether the new system was to blame in the October Lion Air crash, which killed 189 people.

"No one has yet to conclude that the sole cause of this was this function on the airplane," Sinnett said at the meeting, which took place at the Allied Pilots Association headquarters in Fort Worth, Texas. The group represents American Airlines pilots.

Five months after the Indonesia disaster, another Boeing Max crashed, killing 157 people in Ethiopia.

The union recorded the meeting without Boeing's knowledge and shared the audio with media, including CNBC, because it was concerned Boeing wasn't treating the situation as an emergency at the time.

"American Airlines pilots have been pressing Boeing for answers because we owe it to our passengers and the 346 people who lost their lives to do everything we can to prevent another tragedy," APA President Daniel F. Carey told CNBC.

Boeing did not respond to CNBC's request for comment about the recording.

At the November meeting, the pilots said they were not aware of the Max's anti-stall software system, known as MCAS. And they were angry that the system was not disclosed to them until after the October crash in Indonesia.

"These guys didn't even know the damn system was on the airplane — nor did anybody else," American Airlines pilot Michael Michaelis said at the meeting.

Michaelis, the union's head of safety, also told Boeing to push the Federal Aviation Administration to issue an additional emergency airworthiness directive in order to update the software.

"My question to you, as Boeing, is why wouldn't you say this is the smartest thing to do?" Michaelis asked. "Say we're going to do everything we can to protect that traveling public in accordance with what our pilots unions are telling us."

Todd Wissing, another American pilot, was angry the MCAS system was not included in the Max training manual.

"I would think that there would be a priority of putting explanations of things that could kill you," Wissing told Boeing executives.

Sinnett said the company did not believe that pilots needed to know about the software, since they were already trained on how to behave in emergency scenarios.