In an emotional plea, Shamima's sister said she hoped they had only gone to try and bring their friend home, while Amira's father revealed she had told him she was going to a wedding in "a place is a little bit far".
It is believed the youngsters, who attended the same London school, may have been radicalised online.
Commons Leader William Hague used the case to reignite calls for the police and security services to have wider snooping powers.
Days before fleeing, Shamima contacted Mahmood on Twitter but no one alerted her parents, according to the Mahmood family lawyer Aamer Anwar.
"We are aware from contacts with special branch and the police that her social media is regularly checked and regularly monitored. The idea that a 15-year-old should make contact with Asqa, who is regarded as a terrorist, a member of Isis, yet no action is taken ... "
Police are hoping bad weather in Turkey may delay their plans but one Isis figure claimed the girls were already there. The source said the trio were met by a man who took them to the border, where they met another man who helped them cross.