Joshua Hakken, 35, and Sharyn Patricia Hakken, 34, are believed to be traveling with their sons Cole, 4, and Chase, 2, who are the subject of an Amber Alert search, the Orlando TV station Central Florida News 13 reported.
Authorities say Joshua Hakken, facing the loss of custody of the boys, took them from his mother-in-law's home in Tampa Wednesday afternoon after tying her up.
Hills. Co. Sheriff's Office Detective Larry McKinnon said investigators believe Hakken, his wife and his sons are on the 25-foot sailboat he purchased recently.
"They were seen going underneath the John's Pass Bridge and, of course, we all know that leads out into the Gulf of Mexico," McKinnon said.
"They could've gone anywhere. Obviously, north or south along the coast of Florida. There's many inlets all the way up to the Panhandle and south down to Naples. So, we're not only looking along coastline, we'll be looking for any type of intercoastal waterways or inlets they may have been able to get into.
"I don't want to say extensive, but we do know he has some sailing training and some sailing experience, so he is capable of operating that boat."
McKinnon reiterated that authorities consider the parents "armed and dangerous."
He also said it's possible the family returned to shore and is traveling by land again.
Authorities say Joshua Hakken was previously involved in an attempted armed abduction of their children in Louisiana, where he faces multiple drug charges.