The lawyer for the parents of five-year-old British boy Ashya King has said that the couple are desperate, because the media has destroyed their reputation.
Brett and Naghemeh King are being held in police custody after they refused to consent to their extradition to the UK at a court appearance in Spain.
An international search was launched after the couple took Ashya, who has a brain tumour, from hospital in Southampton on Thursday.
Ashya is now in hospital in Malaga after being found with his family in the city on Saturday.
The Kings' lawyer, Juan Isidro Fernandez, spoke to reporters earlier.
Mr and Ms King had their period of detention extended after appearing before a Spanish judge for an extradition hearing earlier.
Brett, 51, and Naghemeh King, 45, were arrested at the weekend in southern Spain on a European arrest warrant.
Their five-year-old son Ashya requires feeding through a nasal tube and a machine, and authorities feared his life could be in danger if he was not given the necessary hospital care.
The family was found on Saturday at a guesthouse on the Costa del Sol following a search operation involving British, French and Spanish police.
Mr King said in a video posted on YouTube that he pulled his son out of hospital because he was not satisfied with the care the boy was receiving.
He said he wanted to seek different treatments abroad that were not offered by the NHS.
The couple were taken to court in a police van this morning, but their hearing was delayed until the early afternoon after their lawyer failed to appear in time.
Relatives have described the decision to arrest Ashya's parents as "cruel".
Ashya's grandmother and his brother have both criticised the way his parents were being treated.
In a video posted on YouTube, his brother, Naveen, defended his parents, saying the family had bought all the necessary medical supplies to ensure Ashya would receive the same treatment as he had in hospital.
Mr King's mother, Patricia King, said it was an "absolute disgrace" that her son and daughter-in-law had been taken away in handcuffs, accused of child neglect.
In his video blog posted on YouTube, Mr King said he had pleaded for proton beam therapy to be used to treat his son but had been told that it would be of no benefit for the medulloblastoma Ashya is suffering.
He also claimed his son's treatment in Southampton seemed like "trial and error" but was told that, if he questioned it, the hospital would seek an emergency protection order.