Rittenhouse was taken into custody Wednesday in Illinois. Since Rittenhouse is 17 years old, he is being held at a juvenile facility in Vernon Hills.
He has been charged as an adult with two counts of murder and one count of attempted murder, along with weapons violations. Authorities plan to extradite him to Wisconsin to be tried.
His two victims have been identified as Joseph Rosenbaum and Anthony Huber.
At Friday morning's court hearing, Rittenhouse's public defender did not waive extradition and asked for more time. He will remain in Illinois custody and the next hearing has been set for Sept. 25.
Rittenhouse's defense team released a statement Friday saying that what the 17-year-old did is a clear-cut case of self defense.
In a written statement, Rittenhouse's lawyers said: "A 17-year-old child should not have to take up arms in America to protect life and property. Kyle is not a racist or a white supremacist. He is a brave, patriotic, compassionate law-abiding American who loves his country and his community. He did nothing wrong."
Rittenhouse's defense team also said legal fees for the teenager will be provided by donations from a non-profit foundation.
"He has made the smart play," Soffer said. "He obviously wants to buy time to get his own lawyer or team of lawyers. He's going to need the very best defense he can possibly get."
WATCH: What Antioch teen said just before deadly Kenosha protest shooting
The night of the shooting, Rittenhouse walked past Kenosha police, hands in the air, but was ignored. He drove home, across state lines, to Antioch and turned himself in on a first-degree intentional homicide warrant from Wisconsin the next day.
There have been question as to why police did not arrest Rittenhouse at the scene. Kenosha Police Chief Daniel Miskinis said his officers had been dispatched to a "shots fired" complaint, not a shooting.
"There were a lot of people in the area, a lot of people with weapons. Unfortunately, a lot of gunfire. What the officers were walking into, or driving into in this case, was a shots fired complaint. Not a shooting, not a person down complaint," Miskinis said. "There was nothing to suggest this person was involved in criminal behavior."
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"Clearly they are not seeing him as a suspect or a threat of any kind," the chief continued. "He's allowed to leave, where he goes to Antioch and turns himself in because we have no idea he's involved."
Independent journalist Richie McGinniss interviewed Rittenhouse at the protest Tuesday night. McGinniss was interviewed by police because he also witnessed one of the shootings.
"People are getting injured. Our job is protect this business. And part of my job is also to help people. If there's someone hurt, I'm running to harm's way," Rittenhouse told McGinniss before the shootings took place.
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"I don't know exactly what his motivations were," McGinniss said. "He did tell me that he was there to protect the peace and to provide medical attention."
McGinniss seen on video attempting to help Rosenbaum after he's been shot. He described what happened next, as he saw someone standing next to him.
"After reviewing the footage, I now realize that was Kyle," he said. "He actually ran away and then ran around the car and came back behind me while I was kneeling down. I didn't realize at the time that was the original shooter."
Huber was shot and killed in the second shooting, which also injured a third person.
McGinniss is a witness cited in the criminal complaint filed by prosecutors in Kenosha County today.
"The way he was describing what his role was seemed very detached from the way he was being perceived. And so that's what I mean when I say he seemed very naive," McGinniss said.
Investigators said Rittenhouse was armed with a Smith and Wesson AR-15 style rifle with a 30-round magazine. Open carry is legal in Wisconsin for adults over the age of 18. There was a large presence of armed civilians at the protest.
Rittenhouse is a former member of a youth police cadet program that included officers from Lindenhurst, Grayslake and Hainseville police departments. He was also enrolled as a fire cadet with the Antioch Fire Department, where the chief said they did not have any issues with him during that time.
WATCH: Deadly protest shooting caught on video
In the video from before the shooting, Rittenhouse identifies himself as an EMT, shouting, "Medical, EMS right here, I'm an EMT." But the department said he was only enrolled in their explorer program for less than a year.
Neighbors say Rittenhouse was interested in law enforcement, often wearing his cadet uniform around the apartment complex where he lived with his mother. He was a student at Lakes Community High School, but administrators there said he did not graduate.
On Thursday, Wisconsin Lt. Gov. Mandela Barnes reacted to the charges and why Rittenhouse was even in Kenosha.
"These armed men who have no connection to even the state. The guy is from out of town. So think about how ridiculous that is," Barnes said. "Who is he accountable to? Nobody. And for him to even be able to shoot somebody and walk away from the scene. You know they talk about finding a knife inside the car, not even on Jacob Blake's person. This guy is carrying a long gun, killed somebody just walking freely was able to get back home to Illinois. Then you know we got much bigger problems on our hands."