Hours later, a Spanish judge ordered the parents' detention for 72 hours while a court in Madrid considers whether to grant Britain an extradition request.
Grandmother Patricia King told the BBC it was an "absolute disgrace" that her son and daughter-in-law were accused of child neglect after they took Ashya from Southampton General Hospital last week. The family says U.K. authorities had refused to give Ashya the kind of treatment he needed.
The family has criticized Britain's health care system, saying he needs an advanced treatment option called proton beam therapy and that it wasn't being made available to him.
King's parents were arrested Sunday in southeastern Spain after a European arrest warrant was issued by Interpol at the request of British police. Their son is receiving medical treatment for a brain tumor. After his parents' arrest, he was admitted to a Spanish hospital.
King says the authorities are "the ones who are cruel, because they have taken poor little Ashya, who is dying of a brain tumor, and they won't let the parents, my son and daughter-in-law, they won't let them see him at all."
Prime Minister David Cameron's spokesman also weighed in on the matter Monday, saying people all over the country have been moved by the family's plight.
British police say the parents, Brett and Naghemeh, are suspected of neglect.
Spanish National Court Judge Ismael Moreno ordered the parents' detention for 72 hours, a court spokesman said. Moreno could have opted to let the parents go free while the extradition case is considered.
The spokesman said Ashya King's parents told the judge they don't want to return to the U.K. They were arrested Sunday in southeastern Spain after a European arrest warrant was issued by Interpol at the request of British police. Their son is receiving medical treatment for a brain tumor and is currently at a Malaga hospital.
The spokesman said the legal process also involves requesting the advice of Spanish doctors and translating legal documents deemed pertinent to the case. He spoke on condition of anonymity because he wasn't allowed to be cited by name in the media.
After the 72 hours expire, the judge could extend their time in detention or release them.
King said in a video posted on the Internet that his research suggests his son would benefit from proton beam therapy, a targeted type of radiation treatment that increases the chance of killing cancer cells by sending a higher dose of radiation directly to the tumor.
Unlike other types of cancer treatment, it doesn't indiscriminately kill surrounding healthy tissue, so there could be fewer long term effects.
In Britain, proton beam therapy is currently only available in the country to treat certain patients with cancer in their eyes. Other countries, including the U.S., Switzerland and Japan, also use proton beam therapy to treat cancers of the spinal cord, brain, prostate, lung and those that affect children.
Britain's health department announced in 2011 it will build two treatment centers to make proton beam therapy available in London and Manchester from 2018. Until those facilities open, Britain will pay for patients eligible for the therapy to go to the U.S. and Switzerland for treatment.
It wasn't immediately clear why health care officials didn't make this option available to Aysha.
Associated Press writer Jorge Sainz in Madrid contributed to this story.