Saturday Night Live and Wayne's World icon Dana Carvey is thanking well-wishers for their support after the death of his 32-year-old son, comedian Dex Carvey, from an overdose last week.

"My wife and I have been overwhelmed by your love, your personal stories, your compassion," Carvey, 68, said in a statement on Saturday.

"We received so many beautiful messages from people who knew Dex. These touched us more than we can ever express in words."

Carvey also said he planned to take a break from work and social media, while he, his wife Paula, and their 29-year-old son Thomas try to "figure out what life looks like now that we are a family of 3."