Hudson's mother and brother were shot to death in their Chicago home last Friday. The bullet-ridden body of Hudson's 7-year-old nephew, who had been missing since the slayings, was discovered Monday morning in the backseat of a sports utility vehicle.
The boy's stepfather has been questioned by police and held on a parole violation, but hasn't been charged in the shootings.
"This is a horrific tragedy and my thoughts and prayers go out to Jennifer and her entire family," People magazine quoted Abdul as saying Monday evening. "The time I had to get to know Jennifer and forge a wonderful friendship with her while she was on 'Idol' was very special to me, and I personally can't imagine a greater loss for any family."
Cowell told the TV program "Extra" he was "horrified" by the news.
"This is an appalling tragedy, Cowell said. "My thoughts right now are with Jennifer, and her family."
U.S. presidential candidate Barack Obama last weekend offered his best wishes to the Hudson family.
"It was heartbreaking," Obama told "Extra" Saturday in recalling how he heard the news of the double homicide and, at the time, the missing child.
"(Jennifer) is somebody who has campaigned for me, she also lives in my community. So, we're really going to have to ... help her and pray for her and her family during this difficult time."