Scott Diver, 16, from Clydebank, West Dunbartonshire, was last seen at home on 17 September.
His father, who is also called Scott, said he was not in any trouble and he just wanted to know he was OK.
The teenager, who is 5ft 7in tall, with a slim build, dark hair and blue eyes, is said to need regular medication.
When Scott last seen, he was wearing a navy blue Adidas tracksuit with light blue stripes down the arms and legs, a white T-shirt and navy Adidas training shoes with grey stripes.
Speaking at a police news conference, Mr Diver said: "Scotty, if you see this please get in touch. You are not in any trouble we just want you home or at least let us know you're safe.
"All the family are missing you especially me and nana and your family in Isle of Man.
"Can I ask anyone who might be helping Scott stay away from home to remember he relies on daily medication which he hasn't had for at least 10 days."
Mr Diver added: "Scotty, we love and miss you and want you home.
"You can contact us on the missing person's text service on 116 000 through phone or text even if you have no credit."
Mr Diver's comments came after police made a public appeal at the weekend in a bid to trace Scott.
On Saturday, one week after he went missing, officers carried out a "stop and speak" operation in the teenager's home town.
They spoke to about 1,000 people at Clydebank's bus station, shopping centre and near Scott's home.
The operation has also seen an air support unit deployed in the area along with a search team.
Insp John Mullen said that anyone with information could contact police at a dedicated email address: scottdiverinquiry@scotland.pnn.police.uk
He added: "Scott is a vulnerable young boy who has just turned 16.
"His family are devastated at his disappearance and I would urge anyone who knows where he is to contact police."

The Conservative group of eight councillors has joined forces with six of the independent members.
The council leader is independent George Alexander, with Conservative James Allan as convener.
Nine SNP councillors were elected in Moray at the recent local elections.
The father of a vulnerable teenage boy, who has been missing from his home for more than a week, has appealed for him to get in touch.
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Moray Council's new administration has been confirmed as a Conservative and independent coalition.