The couple, who have been married for six years, have been plagued by split rumors all week, but have not directly addressed them.
Kutcher sent out a Twitter message with a link to the Public Enemy song, "Don't Believe the Hype," which seemed to be a nod to the breakup buzz.
He sent a subsequent message stating, "When you ASSUME to know that which you know nothing of you make an ASS out of U and ME."
People.com said Kutcher has been wearing his wedding band despite the speculation about his marriage.
He told USA Weekend two weeks ago one of the reasons he signed on to replace Charlie Sheen on the sitcom "Two and a Half Men" was because, "Family comes first."
"It's about being available for everything. I've missed enough and I don't want to be absent for anything else. I just want to be home at night with my wife and family," Kutcher said.
The celebrity Web site X17 posted photos online of Kutcher and Moore arriving for a Kabbalah service Friday.
2014: The Year in Music [PHOTOS]