Clegg told the BBC his "heart goes out" to Brett and Naghemeh King.
"This is a family in a state of real anguish who have taken this exceptional step of moving their sick child to another country because they think that's what is best for their child," Clegg said.
The couple took their son, Ashya, out of Southampton General Hospital last week and travelled to Spain, where they planned to sell a property to pay at least USD 33,000 for proton beam radiation therapy in the Czech Republic or the US.
British prosecutors issued the warrant for an offence of cruelty to a person under the age of 16 years, hours after the Southampton hospital realised Ashya was gone. The Southampton hospital has said more conventional methods have a very high chance of succeeding.
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"I personally think that throwing the full force of the law at Mr and Mrs King, who appear to be doing what they believe to be best for their own family, I don't think is an appropriate thing to do," Clegg said. "But that, at the end of the day, is for the police and (prosecutors) and others to decide."
The parents' Spanish lawyer, Juan Isidro Fernandez, has said Ashya's 23-year-old brother is with him at a Malaga hospital.