The 17-year-old from Antioch, Illinois, requested to waive his presence at the extradition hearing. His lawyer, however, did not waive the extradition to Wisconsin request during the short virtual court proceeding Friday morning, but asked for more time.
A hearing on the status of his extradition has now been set for Sept. 25.
Rittenhouse has been charged in Wisconsin with two counts of homicide, one count of attempted homicide, two counts of recklessly endangering safety and one count of possession of a dangerous weapon. He is currently being held in Lake County, Illinois.
The violence occurred late Tuesday night near a gas station in Kenosha, some 40 miles south of Milwaukee, amid a third night of protests over the police shooting of Blake. One of the victims in the deadly shooting was shot five times, including in the head, and the other was shot in the chest, according to a criminal complaint. A third gunshot victim was taken to the hospital with serious, but non-life-threatening injuries, according to police.
Rittenhouse surrendered to authorities in Antioch, Illinois, on Wednesday, local police said.
Social media accounts allegedly linked to Rittenhouse are part of the investigation, authorities have said. Those now-deactivated accounts contain references of support for President Donald Trump and support for Blue Lives Matter.
Trump's reelection campaign issued a statement Wednesday night distancing itself from the alleged shooter.
"President Trump has repeatedly and consistently condemned all forms of violence and believes we must protect all Americans from chaos and lawlessness. This individual had nothing to do with our campaign and we fully support our fantastic law enforcement for their swift action in this case," Trump 2020 campaign communications director Tim Murtaugh said via the statement.
Moreover, social media video of Rittenhouse, who is white, passing police with his assault-style rifle shortly around the time of his shooting rampage has caused further outrage -- especially as Blake was shot seven times in the back by police without possession of a gun.
ABC News' Wil Steakin and Whitney Lloyd contributed to this report.