The incident sent a number of social media users into an uproar, with some calling the policy sexist and discriminatory against women.
"A @united gate agent isn’t letting girls in leggings get on flight from Denver to Minneapolis because spandex is not allowed?" she wrote on Twitter.
"A 10-year-old girl in gray leggings. She looked normal and appropriate. Apparently @united is policing the clothing of women and girls," she added in another tweet.
"We heard the gate agent say, 'You know, these aren't my rules. I just enforce them,'" Watts told ABC News. The two girls, who weren't identified, "looked very panicked," according to Watts.
Watts, a mother of five and the founder of Moms Demand Action for Gun Sense in America, said of the apparent dress code prohibiting leggings, "To me, that seems like a pretty sexist policy."
A spokesman for United confirmed that two teenage passengers were told they could not board a flight from Denver to Minneapolis because their leggings "were not in compliance with dress code policy for company benefit travel," a program that lets United workers and their family members travel free on a standby basis.
"There are different rules for these privileges because people are flying for free," he said in an emailed statement Sunday.
United Airlines issued a dozen or so tweets in response to users who were upset about the incident.
United said the teens waited for the next flight and eventually got to travel under the benefit program. For "regular customers," the airline said in the statement, "leggings are welcome."
In one tweet, the company said it reserves the right to deny service to "passengers who are not properly clothed via our Contract of Carriage."
ABC News' Will Gretsky contributed to this report.