The demand comes after the Metropolitan Police wrongly claimed the families had known that a close friend of the girls was already in Syria before they disappeared from London last month.
The families insist that if they had known, they may have been able to stop Shamima Begum and Amira Abase, both 15, and Kadiza Sultana, 16.
They flew to Istanbul on February 17 and according to Sky News reports are now in a house in the Syrian city of Raqqa.
"It is precisely the failure to communicate this key piece of information which disabled the family from intervention in the children's plans," he said.
On Friday, the girls' families criticised police for not passing on "vital" information, they say may have helped them to intervene in the trio's plans.
It later clarified that following further discussions with Bethnal Green Academy in east London school it emerged that the deputy head had only informed them that the girl was missing.
Police said all of the girls had been treated as potential witnesses who may have had information about their friend.
In February, the girls were also given letters to take to their parents asking permission for counter-terrorism detectives to take handwritten statements about their friend's lifestyle and beliefs.
Yesterday Met Police Commissioner Sir Bernard Hogan-Howe admitted that "with the benefit of hindsight" officers should have communicated directly to the families.
As many as 60 young British women including many teenagers are believed to have left UK to become the brides of jihadists fighting in Syria and Iraq.
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