Melissa Reid, 20, from Lenzie near Glasgow, and Michaella McCollum, also 20, from Dungannon, Co Tyrone in Northern Ireland, were stopped with 24lb (11kg) of cocaine hidden in food packets in their luggage while trying to board a flight to Spain last month.
The pair claim they were forced to carry the drugs by an armed gang who threatened them and their family members.
They have reportedly told the Peruvian authorities they were working in Ibiza and did not meet before they were both kidnapped at gunpoint and forced to travel to Majorca.
Ms Reid's father, William, told ITV's Daybreak: "The Peru element of the story I can follow and understand. It's the Ibiza end I would like more clarification on. I'm still not entirely sure how she left Ibiza to go to wherever it was - Madrid or Majorca and then on - so I would like more help from the Spanish authorities and the British police."
Both women are being held in a classification unit at the notorious Virgen de Fatima jail in Peru's capital Lima. The prison houses some of the country's most dangerous criminals.
But Mr Reid, who visited the pair last week, said they were calm and doing "as well as can be expected in their current predicament".
He added: "The current prison conditions are OK and not as bad as we were led to believe prior to going over to Peru, so that was a worthwhile visit for that reason alone: to get some comfort they have a bed and some space.
"They're not eight to a cell, etcetera, or sleeping in corridors [which] we were told was possible. But if they're moved to another prison that could change."
Mr Reid reiterated his belief the women should plead guilty so the case is dealt with sooner.
"That is based on having been over in Peru and understanding more about their legal system," he said. "They appear to operate on the basis you're guilty unless you can prove your innocence."
He added: "Pleading guilty means your case at least would come to court and you'd be given a sentence potentially within six months. If you continue down the not guilty route it can take two to three years before your case even comes to court."
It emerged on Sunday that the Peruvian prosecution lawyer who is building the preliminary case against Ms Reid and Ms McCollum says he does not believe a word of their story.
Dr Mendoza Abarca said the women's excuses were "very well practised"; they had been coached in what to say; and their "demeanour did not suggest they had been threatened".
The case is now in the hands of the judiciary, but Dr Abarca has been privy to all the evidence in the first 15 days of the case.
Both women face a maximum term of 15 years if convicted of drug smuggling. They are the only two foreigners in the Virgen de Fatima prison, are said to dislike the food available to them, and have gone into "survival mode" to cope with their new lives.