A five-year-old boy with a brain tumour, taken from hospital without doctors' consent, must receive "the very best and most appropriate" medical care, the Prime Minister's spokesman said.
Ashya King was taken by his parents from Southampton General Hospital last Thursday to seek a new treatment that is not available on the NHS.
Asked whether David Cameron sympathised with the boy's parents , the spokesman said: "I think people up and down the country will understand and be moved by the grave illness from which Ashya is suffering.
"First and foremost, the priority must be that he receives the very best and most appropriate medical care.
"Of course, I am sure that every parent wants to do the best for their child. That is probably the most human of human instincts."
The head of the police force which applied for a European Arrest warrant against the parents of Ashya King has now urged their release.
A British mother whose son's life was saved by proton therapy has told ITV that she defied NHS doctors' advice to pursue the treatment.
The parents of Ashya King said they took him out of a hospital to seek proton beam treatment which is not available under the NHS.