A video posted online showed a red sport utility vehicle plowing at speed through the parade, appearing to run over more than a dozen people before crowds ran from sidewalks to offer assistance.
Thompson said an officer fired shots at the vehicle in an attempt to stop the carnage. Another video on social media appeared to show police firing on the vehicle as it crashed through street barriers. Police did not believe shots had been fired from the vehicle, Thompson added, contrary to earlier reports.
Belen Santamaria, her husband, and their three-year old daughter were planning to join the parade with their Catholic Church. But Santamaria, a 39-year old Mexican factory worker, woke up on Sunday with a backache, so the family watched the procession from the sidewalk instead.
"The SUV came by at full speed," said Santamaria. "Then I started to hear people screaming."
She hid in a restaurant with their daughter while her husband, 39-year old delivery worker Jesus Ochoa, ran ahead to try to help injured people. He said he heard through other members of their church that roughly 10 members of the congregation, mostly Latinos and both adults and children, are injured.
"I was going to be there, walking," Santamaria said. "The SUV would have hit us too."
Dance Groups Hit
A woman told Milwaukee's Fox6 TV station that the SUV hit a dance team of girls between 9 and 15 years old. She said the immediate reaction was silence, followed by screaming, running and checking on those injured, Fox6 reported. Video on social media showed small groups surrounding injured girls with white pompoms scattered around.
One witness said the driver also hit a group of "Dancing Grannies" and at least one person flipped over the hood of the SUV, according to Milwaukee's WISN-TV, an ABC affiliate.
"Members of the group and volunteers were impacted and we are waiting for word on their conditions," the Milwaukee Dancing Grannies said on their Facebook page. "Please keep the Grannies, all those injured, and all those who witnessed this horrible event in your thoughts and prayers."
Another witness estimated the SUV was going about 40 mph (64 kph) when it hit the crowd parading down the street, the TV station said.
"As we were walking back in between the buildings ... we saw an SUV cross over, just put the pedal to the metal and just zooming full speed along the parade route. And then we heard a loud bang, and just deafening cries and screams from people who are struck by the vehicle," Angelito Tenorio, an alderman in nearby West Allis, told the Milwaukee Journal Sentinel.
The local CBS affiliate later showed a picture on Twitter of what appeared to be the red SUV involved with its hood crumpled and front fender hanging off, parked in a driveway.
President Joe Biden was briefed by aides about the events, a White House official said.
"The White House is closely monitoring the situation in Waukesha and our hearts go out to everyone who has been impacted by this terrible incident. We have reached out to state and local officials to offer any support and assistance as needed."
Photos and videos of Waukesha circulating on Twitter showed police cars and ambulances crowding a street decked out with Christmas lights in the aftermath of the incident, which occurred shortly after 4:30pm (2230 GMT). People bundled up against the cold huddled on sidewalks as dusk fell.
The Children's Wisconsin hospital said on Twitter it had received 15 patients as of 8:00pm, with no reported fatalities at that time.
Schools would remain closed on Monday for grades 4K-12 and additional counselors would be available for students who may need support services, the district superintendent of schools said.
In 2015, four people were killed and 46 injured in Stillwater, Oklahoma when a woman drove into a crowd watching the homecoming parade for a football team.
A truck was deliberately driven into a Christmas market in Berlin, Germany in 2016, killing 12 people in an attack linked to Islamic State.