Aqsa Mahmood, 20, travelled to Syria from her Glasgow home to become a "Jihadi bride" in November 2013.
The Daily Mail reported she had been in touch with at least one of the three London girls, who are aged 15 and 16.
The trio are thought to have flown to Turkey in an attempt to enter Syria.
Shamima Begum, 15, Kadiza Sultana, 16,  and an unnamed 15-year-old girl, who all attended Bethnal Green Academy in Tower Hamlets, travelled to Turkey on Tuesday.
They were interviewed by police after another girl from their school went to Syria in December but were not considered as a risk.
In a statement released through their lawyer Aamer Anwar, the Mahmood family said they were "full of horror and anger that their daughter may have had a role to play in the recruitment of these young girls to Isis".
They also sent a message to Aqsa: "You are a disgrace to your family and the people of Scotland, your actions are a perverted and evil distortion of Islam.
"You are killing your family every day with your actions, they are begging you stop if you ever loved them."
The statement also said the UK security services had questions to answer.
It added: "Aqsa's social media has been monitored since she disappeared over a year ago, yet despite alleged contact between the girls and Aqsa, they failed to stop them from leaving the UK for Turkey, a staging post for Syria.
"Sadly, despite all the government's rhetoric on Isis, if they can't even take basic steps to stop children leaving to join Isis, what is the point of any new laws?"
Privately educated Mahmood travelled through Turkey to Aleppo in Syria, where she married an Islamic State fighter.
She was reported to have later encouraged terrorist acts via a Twitter account under the name Umm Layth. The account has since been deleted.
Speaking in September, her parents Khalida and Muzaffar Mahmood said their daughter had attended Craigholme School, then university and was "well integrated into society".
They also said she was brought up "with love and affection in a happy home" and appealed for her to come home.
Relatives of a Scottish woman who is suspected of helping to recruit three missing London teenagers to Islamic State (IS) have said she is a "disgrace to her family".