Funeral arrangements are pending.
In a statement, David Alvey, mayor of the Unified Government of Wyandotte County and Kansas City, said the city is saddened by the "senseless shootings" of the deputies.
Bailiff said the inmate was being taken across the street from the jail, to the services building, for a court hearing.
Terry Zeigler, the police chief of Kansas City, Kansas, said he couldn't release the name of the inmate suspected of shooting them Friday because he hasn't been charged.
Fielder faced trial twice for the alleged murder of a 22-year-old.
Several law enforcement departments offered words of support and prayers for Wyandotte County on social media.
Rohrer had been with the department for seven years and had moved to the court transport division in January. King, 44, served for 13 years. Bailiff said she was not sure whether the suspect was shot by one of the deputies or someone else who responded to the incident.
"It is very possible that with their own firearm, they were both shot", Wyandotte County sheriff's Maj.
Bailiff said the investigation is now being handled by the police department in Kansas City. "It's a tremendous, great loss to our agency".
'Our thoughts and prayers go out to our brothers and sisters in Wyandotte County. "We just ask that everyone first of all keep everyone in your prayers, from the families to our community members, to our deputies to their families".
A candlelight vigil will be held at 8 p.m. Sunday in front of City Hall. They also said it was too early in the investigation to give specific details of how the shootings could have happened. "We always evaluate procedures, but we did confirm that they did follow proper procedure".
"This is a courthouse building, there is video".
The inmate was also shot during the confrontation in a gated area near the Wyandotte County Courthouse and was taken to a hospital. Bailiff said the second inmate, who was not identified, was unharmed.