The Lake County State's Attorney's Office will seek to hold Karels without the possibility of a cash bond, and that motion will be heard in court on July 13, prosecutor Jeff Fackham said.
Karels was arrested after leading police on a chase that ended in a crash Monday at an Interstate 80 bridge in Joliet, Round Lake Beach police Chief Gilbert Rivera said at a news conference Tuesday.
Karels was hospitalised after the crash but has since been released, prosecutors said.
Rivera said the parents shared custody of the children but did not live together. Rivera said he did not know their marital status.
After the crash in Joliet, Karels told first responders he was responsible for his children's deaths and had attempted to kill himself before fleeing the home, Rivera said.
Officers found the man's blood in the house from his attempts to hurt himself, Rivera said.