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.
Ashya King's parents told the Daily Mail they fled the UK after being told NHS treatments would leave him with life-long disabilities.
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.