Questions about the state of the couple's marriage emerged recently when Moore posted a series of cryptic messages on Twitter.
Kutcher responded by first tweeting a link to the Public Enemy track 'Don't Believe The Hype' and then warned his fans not to "assume" anything.
Moore reportedly met with divorce attorneys last week amid reports that Kutcher had spent the pair's sixth wedding anniversary with a woman believed to be 23-year-old Sara Leal.
The couple attended Yom Kippur services together at LA's Kabbalah Centre on Friday, before going camping near Cachuma Lake.
Kutcher and Moore were snapped building a fire and preparing food at the campsite on Saturday.
Kabbalah instructor Yehuda Berg and Kutcher's good friend Eric Buterbaugh were also present on the trip.
Kutcher and Moore have offered no direct comment on their marriage yet.
> Ashton Kutcher, Demi Moore spotted together amid split rumours