Staff members were taken hostage at around 2pm local time, although two have now been released as prisoners continue to make demands to authorities.
The inmates have been making the demands through a hostage on a call to media outlets.
"I'm just doing what I'm being told to,” he said.
“I’m just trying to help, ma'am. They just need somebody to hear their demands.”
Two hostages were released several hours apart although officials believe two prison employees are still being held.
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The inmates have called for better treatment and reform of the way the prison is run.
Sergeant Richard Bratz, a spokesman for Delaware State Police, said: "Working with the Department of Correction, the FBI and the Delaware State Police will continue negotiations to obtain a peaceful and safe resolution."
He added that one of the released hostages has been taken to hospital with non-life-threatening injuries.
SWAT teams arrived on scene along with dozens of police vehicles and ambulances, while helicopters spent hours circling the scene.
— #J20 (@Delo_Taylor) February 1, 2017
Ambulance outside the James T. Vaughn state correctional facility in Delaware
The prison houses 2,500 inmates in minimum, medium and maximum security.
William Carson, a member of the Delaware House Corrections Committee, said he had been told it was an “apparent hostage situation.”
“The inmates have taken over a building,” he told the Delaware News Journal.
The hostage situation broke out in Building C of the complex, which houses between 120-150 inmates.
— KTLA (@KTLA) February 1, 2017
It is also where maximum security inmates transition to medium security.
Every other prison in the state of Delaware has been placed on lockdown in response.
At the same prison a councillor was taken hostage and raped for nearly seven hours at the same prison in 2004.
The standoff ended with the attacker being shot.