Missing Belgian tourist Theo Hayez was last seen on May 31 at a hotel in Byron Bay. (AFP)

The father of an 18-year-old Belgian backpacker made a heart-rending appeal for help finding his son Monday, as Australian police admitted they were "baffled" by his disappearance from a picturesque surf town.

Theo Hayez was last seen on May 31 at a hotel in Byron Bay -- some 750 kilometres (470 miles) north of Sydney.

New South Wales state police were alerted to his disappearance on June 6 after he failed to return to the hostel where he was staying and have scoured bushland and off the coast to no avail.

"I promised Theo's little brother, Lucas, that I would bring his brother home. Please, help me keep my promise to him," father Laurent Hayez said, struggling to be heard through tears.

Meanwhile, police superintendent David Roptell announced the release of footage of the teenager buying alcohol at a store on May 31 in the hope it would jolt people's memories.

"Hopefully if people were in the area at that time... they may have recognised or have some information that is leading to the disappearance of Theo Hayez," Roptell said, adding: "We are baffled... because that is all we have."

"Homicide police are one of the lines of inquiries. We're open to anything."

Roptell said it was "out of character" for Hayez to be missing and he had been due to return home after visiting Byron Bay.

Hayez is believed to have used the messaging app WhatsApp the night he disappeared and his father, who has travelled to the town to meet police, called for his account to be shared with investigators.

"We understand the politics about confidentiality and respect that. However, this is a question of providing assistance to a person in grave danger... Every minute counts," he said at the same press conference as he broke down in tears.

Hayez's passport and personal belongings were all left at the hostel, and police believe he has not made any financial transactions since his disappearance.