The group said the confrontation was carried out by members of an organization called Open Carry Texas. The statement said that nearly 40 armed men and women, including some with semi-automatic rifles, arrived in the parking lot outside the restaurant after learning of the small gathering on Facebook.
Moms Demand Action posted a photo on Facebook showing the armed group, including some men kneeling in the front.
"Our mom members and restaurant customers were terrified by what appeared to be an armed ambush," the group said in a statement. "Sadly, these bullies are attempting to use guns to intimidate moms and children and to infringe on our constitutional right to free speech. But Moms Demand Action will not be deterred. The desperate actions of this vocal minority only fuels our determination to fight for gun reform in Texas and across the country. Change will come."
A spokeswoman for Moms Demand Action told TPM on Monday the group plans to file a police report later in the day.
The group was founded in December in response to the Sandy Hook Elementary School massacre in Newtown, Conn.
Photo provided to TPM by Moms Demand Action