"This news has left me heartbroken," said Sigler, who played daughter Meadow to the late actor's Tony Soprano on HBO's The Sopranos, in a statement. "I can only imagine the pain his family feels at this time, and my heart goes out to them, especially Deborah, Michael and Liliana."
Sigler added, "I spent 10 years of my life studying and admiring one of the most brilliant actors, yes, but more importantly one of the greatest men. Jim had the ability, unbeknownst to him, to make you feel like everything would be alright if he was around. I treasure my memories with him and feel so honored that I was an up close witness to his greatness."
Meanwhile, Iler, who portrayed Gandolfini's son A.J. on the series, penned a heartfelt message on his Facebook page.
"I haven't cried in years and now I can't stop ... Please tell me this is all a bad dream ... I love you so much james and always will," he wrote.
Drea de Matteo, who played Adriana on The Sopranos, also released a statement regarding Gandolfini's death.
"Fughedabout losing one of the best actors of our time... we lost so much more," the actress said. "Anyone from the Soprano family will tell you he was one of the most generous, real and humble human beings ever...with a presence that could shatter planets when he walked into a room. A King through n through. So very sorry for his family."
Several of the show's crew members ttook a moment to remember the actor as well, saying in a statement: "He was the head of the Soprano family on and off the screen...he took care of us all no mater who we were. His generosity was limitless. There are no words to truly describe how much he was loved & how much he will be missed!!"
Gandolfini passed away in Rome on Wednesday after suffering an apparent heart attack. He was 51.
The actor won three Emmy Awards, three Screen Actors Guild Awards and a Golden Globe for playing the iconic TV mob boss.