Jim Forrest struggled to hold back tears as he appeared at a police press conference to urge the pair to come home, saying: "Please, please get in contact."
His emotional appeal came as it emerged a European arrest warrant has been issued for his Inverurie, Aberdeenshire-born son.
Looking exhausted and tense, Mr Forrest said: "Hi Megan, hi Jeremy, I hope this message reaches you and you are both okay.
"There are a lot of people back home that are desperate to hear from you. All I am asking is for one of you to make a call, send an email, so we know you are both safe.
"We are all here for you both."
He said he was worried that his "caring" but "vulnerable" 30-year-old son could "flip".
Speaking at the same press conference, Chief Inspector Jason Tingley, of Sussex Police, said the force was liaising with all European countries.
Mr Forrest, from Petts Wood, south-east London, appeared alongside his tearful wife Julie to make the appeal a week after the pair boarded a ferry to France.
Megan was reported missing at about midday last Friday after she failed to turn up at the Bishop Bell Church of England School in Eastbourne.
Her family revealed that Megan had been receiving extra-curricular maths lessons since before the summer. But they did not suspect any relationship between her and Jeremy Forrest, a married would-be musician.
The last sighting of the pair was from CCTV cameras on board a ferry at 9.30pm last Thursday. It showed them arm-in-arm and hand-in-hand.
Forrest's parents sat with their heads in their hands next to Mr Tingley as he said the warrant meant their son could now be arrested and Megan taken into care.
Mr Tingley said there had been rumoured sightings and information passed to police from countries throughout Europe.
He said as it had been thought the couple would return to the UK on Sunday, when they had return ferry tickets booked.
The process of applying for a European arrest warrant had not started until Monday and it had been granted on Tuesday., which was not as "quickly as we might have liked," he said.
Mr Tingley added: "This has probably not gone the way that Megan or Jeremy expected.
"Jeremy will be aware that he has questions to answer, and making contact with us is the best way he can do this.
"As part of the process of working with the French authorities, we have secured an international letter of request and a European arrest warrant.
"These orders, which have been obtained with the help of the Crown Prosecution Service, enable us to work with the European authorities and are in relation to an offence of child abduction. This means taking Megan without the consent of her parents."
He said an officer from the Sussex force had gone to Paris to work with French police searching for the pair.
Mr Tingley refused to discuss whether Mr Forrest was being looked into before they set off to France.
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