Road rage erupted outside a Montgomery County mall Thursday, ending with two people taken to the hospital with knife wounds, authorities said.

Two cars were involved in the conflict, each with a young child inside, law enforcement officials said. The children were not injured. A 28-year-old woman received serious injuries and a 31-year-old man received wounds that were described by police as non-life threatening.

“The stabbings appeared to follow an incident of road rage,” said a law enforcement official who spoke on the condition of anonymity because the investigation was continuing.

Thursday night, police identified the suspect as David B. Goldberg, 24, of the 11600 block of Milbern Drive in Potomac. After the altercation, he was found on the top of a nearby parking deck, and police said that his 2-year-old daughter was in the vehicle.

Goldberg was charged with two counts of attempted first-degree murder and two counts of first-degree assault, among other charges. He was being held without bond. Police say he was driving a Mitsubishi, and the other car was a dark-colored sedan.

The incident began about 2 p.m., when officers were called to a parking lot outside the Westfield Montgomery Mall, which is near the Capital Beltway, police said.

In addition to the two victims, there were also a young child and another female in the dark sedan, officials said.

Police identified the weapon as a folding knife. A third vehicle was involved in the incident, tangentially, when the Mitsubishi apparently crashed into it, police said.

Lt. Oneil Ormsby, a Montgomery police officer on the scene, stressed that motorists should not get out of their cars to argue with one another and that if they feel threatened, they should call for help. “If you have any concerns for your safety, call us at 911,” he said.