The police said they had "positive information" to suggest that Ashya King and his family could be in Spain, where they have "strong links" to the Marbella area on the south coast.
King's parents, who are Jehovah's Witnesses, drove him away from a hospital in Southampton in southern England on Thursday and were seen boarding a ferry to Cherbourg in France.
Interpol has launched a missing persons alert following a request from British police, who are leading the search.
"What that will do is, when we find Ashya and his family, it will allow us to talk to his parents about what happened. Clearly we need to find out what their motive is in taking Ashya," he added.
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He said that the warrant was based around "neglect" but added, "That does not necessarily mean they would be charged with that offence. It purely gives us the power to arrest and then we'll be able to speak to them."
Spanish police said today that they were looking for the missing child on the Costa del Sol.
The boy is fed through a tube and the batteries on his feeding system will have expired. Police have a "shrinking window" to find him, Shead said.
He said it was unknown whether the King family had any spare batteries or any way of recharging one.
"I'm sure what they are doing, they think they are doing in Ashya's best interests. But let me assure you, the advice I've been given from doctors today is this is a really quite serious situation for Ashya," he added.