Hampshire Constabulary makes "no apology for the police being as proactive as we can to find Ashya", Assistant Chief Constable Chris Shead said.
He said medical experts expressed "grave concern" for the five-year old boy.
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.