According to a statement allegedly issued on behalf of the group said said it was "outrageous" to suggest the family had been kidnapped and forced to join the group, reported BBC.
The statement said, "The family had arrived in a land that was "free from corruption and oppression" and had not been "commanded" to join by a single person but by the "Khalifah of the Muslims".
It called on all Muslims to join them and "hasten to the obedience of Allah".
The family from Luton went missing on May 17. Earlier police said they may have travelled to Syria.
However the report is yet to be verified.
ISIS militants conquered large swathes of Iraq and Syria last year, in a brutal campaign to establish an Islamic caliphate.