The statement, released by her representatives to People magazine, reads, "Lea is deeply grateful for all the love and support she's received from family, friends, and fans. Since Cory's passing, Lea has been grieving alongside his family and making appropriate arrangements with them.
"They are supporting each other as they endure this profound loss together. We continue to ask the media to respect the privacy of Lea and Cory's family."
Monteith, 31, who played heartthrob Finn Hudson on the Fox hit musical series "Glee," was found July 13 at Vancouver's Fairmont Pacific Rim Hotel. He checked into the hotel July 6, and was expected to check out July 13. When Monteith missed his checkout time at noon, hotel staff went to his room and discovered his body. Police ruled out foul play early on.
Immediately following his death, Michele's representatives said in a statement, "We ask that everyone kindly respect Lea's privacy during this devastating time."
As previously reported, Monteith checked into rehab for substance abuse in March 2013.
Michele previously told People magazine, "I love and support Cory and will stand by him through this. I am grateful and proud he made this decision."
Click here to read more reactions from celebrities, co-stars and friends of the late actor Monteith.