The Association of Flight Attendants, which represents thousands of cabin crew on United, Alaska and a host of other airlines, commended Alaska Airlines for investigating the incident but warned that flight attendants lack the proper training and guidance to deal with such issues.

Sexual harassment in air travel gained more visibility late last month after Randi Zuckerberg, a media executive and sister of Facebook founder and CEO Mark Zuckerberg , reported she was sexually harassed on an Alaska Airlines flight.

In a letter to staff on Monday, Oscar Munoz asked employees to "all join with me in making a commitment to zero tolerance for sexual harassment of any of our colleagues and customers."

Its flight attendants' union calls it a "silent epidemic." As high-profile allegations of sexual harassment become a near-daily occurrence, United Continental Holdings' CEO is trying to get ahead of the problem.

"The industry and regulators need to come together to develop policies and tools to respond to these incidents on board," union president Sara Nelson said in a statement to CNBC. A union survey found the majority of flight attendants "have no knowledge of written guidance and/or training" on this issue," she added.

Munoz's letter comes after the airline faced several public relations black eyes this year. Munoz and United faced a public outcry in the spring after a botched apology for the violent dragging of passenger David Dao off one of its flights to make room for commuting crew.

Flight attendants themselves are often victims of sexual harassment, Nelson wrote in a Dec. 8 op-ed in the Washington Post.

"Even today, we are called pet names, patted on the rear when a passenger wants our attention, cornered in the back galley and asked about our 'hottest' layover, and subjected to incidents not fit for print," she wrote.

Flight attendants are also tasked with handling customers who report sexual harassment on board by fellow passengers. Crew are often encouraged to de-escalate situations during flights and may try to separate passengers in the case of a problem. Flight diversions are costly.

Nelson wrote that flight attendants "never had reason to believe that reports of the sexual harassment we experience on the job would be taken seriously, rather than dismissed or retaliated against" and called on chief executives to speak out.

Munoz, in his letter, said he was adding his voice to Nelson's and those of team members "who adamantly believe that sexual harassment, inappropriate behavior, intimidation or predation have absolutely no place anywhere in our society — including, and especially, in our industry and on our aircraft."