Naghmeh and Brett King, who sparked an international manhunt last summer by removing their son from a UK hospital without medical consent for brain tumour treatment abroad, told The Sun newspaper Ashya was now cancer-free.
However, the Czech clinic where Ashya was treated have said there is no guarantee he will not suffer a relapse.
Director Iva Tatounova told Sky News: “We haven’t seen the scans that you are talking about first of all.
“Second of all, nobody will ever say somebody is 100% cancer free, so we have to be very cautious about that as well.
“But we have treated more than 60 children here in Prague with brain tumours and all of the kids are doing very well.”
Mrs King described Ashya’s recovery as “a miracle”.
“If we had left Ashya with the NHS in Britain, he would not be with us today,” she told The Sun.
“He was too weak and would not have survived.”
Ashya was finally allowed to undergo treatment at the Proton Therapy Centre (PTC) in Prague for brain cancer after a long legal battle fought by his parents.
Mr King said his son’s condition now justifies their actions in taking him from Southampton General Hospital last August, to Spain where they have a holiday home.
He said: “We have saved his life”, adding that they would do the same thing again if they felt they had to.
The Kings were arrested in Spain and spent several nights in prison away from their son, before being released.
A High Court judge approved the move to take Ashya to Prague for proton therapy, which the PTC said is more effective than the radiotherapy Ashya was being offered on the NHS.
It limits the collateral damage of radiation to other vital organs, such as the heart and liver in Ashya’s case.
This would lead to less severe long-term side-effects including heart and breathing problems.
The therapy was not available for him on the NHS, although the health service later agreed to fund Ashya’s treatment.
The family, who have previously spoken of their apprehension over returning to the UK for fear social services would get involved, are staying in Marbella where Ashya will continue his recovery.
The Sun quoted a report from the PTC as saying the oncology department “could speculate that Proton Therapy received could be sufficient to sterilise sites of possible future relapses of the tumour and chemotherapy could deteriorate the quality of life of Ashya”.