"The entire Glee family and I are deeply saddened by this tragedy," Rivera said. "Cory was and always will be a part of my own family and a good friend.
"He was a special part of this world and will forever be missed. My heart goes out to Cory’s family and Lea [Michele, "Glee" star and Monteith's girlfriend] and while we are grateful for everyone's well wishes, privacy during this time of grief is greatly appreciated."
Rivera was part of the original "Glee" cast along with Michele, Chris Colfer and Jenna Ushkowitz.
Monteith was found dead in a Vancouver hotel room on Saturday. The cause of death has not yet been released, but authorities are expected to complete his autopsy and toxicology reports Tuesday.