Megan Stammers, 15, was last seen on Friday and "is believed to be in France with Jeremy Forrest from Ringmer, East Sussex", according to a statement from Sussex Police.
"Our inquiries have shown that the pair left the UK through Dover at some point after 9.30 p.m. (2030 GMT) on Thursday 20th September after boarding a ferry in Jeremy's black Ford Fiesta," Chief Inspector Jason Tingley of Sussex Police told a press conference on Monday.
"They were expected to return yesterday, Sunday 23rd September, during the late evening. The scheduled ferry and the passenger ferry were checked but they were not on either."
Tingley added that subsequent ferries had been checked with no success.
Making a direct appeal to Forrest, Tingley said: "Right now our priority is to know that Megan is safe and I would ask you to do the right thing and make contact with us."
Megan's parents made an emotional appeal for their daughter to return.
"Sweetheart, I don't care what you've done or why -- I just want you home," her weeping mother Danielle Wilson said.
She described her daughter as affectionate and intelligent. "She's never brought trouble to my door," she added.
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Her stepfather Martin Stammers said: "This is so out of character for her."
Forrest, who plays in a rock band under the stage name Jeremy Ayre and is married to a 31-year-old woman, had hinted at a "moral dilemma" on his blog four months ago.
Police have said they do not believe Megan is "at risk" but they are seeking to reunite her with her family.