'Now you question every restaurant you walk into': Group speaks out after alleged racist incident at Buffalo Wild Wings

The attorney representing a group that said they were asked to move seats at an Illinois Buffalo Wild Wings because of their race is calling for the company to be "trailblazers" when it comes to standing up to racism.

"We are hoping, in fact, we are expecting that they will be good corporate citizens and take the opportunity to do the right thing … We are looking to change things," attorney Cannon D. Lambert said at a press conference Tuesday.

Justin Vahl and Marcus Riley said at the press conference that they were among a group of 18 people, including children aged 5 to 12, who were asked to go to another table because a customer didn't "want to sit around black people."

"Now you question every restaurant you walk into," Riley said.

The alleged incident occurred on Oct. 26 at a Buffalo Wild Wings in the Chicago suburb of Naperville.

Vahl and Riley said the group eventually left after being asked multiple other times to move.

"A couple of the kids asked what was going on, if they were getting kicked out," Riley said.

The restaurant franchise said in a statement Monday that the employees involved were fired and the customer "who exhibited the inappropriate behavior" was banned from all Buffalo Wild Wings locations for life.

"Buffalo Wild Wings values an inclusive environment and has zero tolerance for discrimination of any kind … Buffalo Wild Wings will conduct sensitivity training throughout our Chicagoland sports bars in response to this incident," the statement read. The company did not respond on Tuesday to ABC News' request for further comment.

Lambert urged the company to do more.

"We are not surprised that you are instituting sensitivity training. We are surprised there wasn’t any already in place," Lambert said at the press conference.

"If you're telling us you're banning a couple, well, we'd like to know how," Lambert added.

The attorney said Buffalo Wild Wings should establish an accountability system and adopt new procedures when hiring potential employees, including asking candidates how they would deal with a racially-charged situation.

A lawsuit against Buffalo Wild Wings has not yet been filed, and Lambert said there would be no need to do so if the company agreed to speak with the group and admit "this should have never happened."

Ashley Smith, another member of the party during the alleged incident, was overcome with emotion as she tried to speak about how the children are holding up.

"To see them try to understand is hurtful. They should not have to understand. You look at these boys and they are all different and they need to know that’s okay," Smith said through tears.

Six children were present for the press conference and could be seen crying after Smith spoke.