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29 September 2015, 16:49 | Updated: 29 September 2015, 18:21
The family of Aqsa Mahmood, one of the four British jihadis hit with international sanctions, has described the Government's move as "useless grandstanding''.
Mahmood, 21, left her Glasgow home in November 2013, travelling to Syria where she is believed to be a key figure in the female brigade established by Islamic State to enforce Sharia law.
The former university student has used social media to promote IS and has reportedly said she would rather die in Syria than return to the UK.
In a bid by the Government to stem the recruitment of home-grown jihadis, Mahmood, two men and another woman have been placed under UN sanctions meaning the group are subject to a global asset freeze and travel ban.
However, Mahmood's relatives said they believe a ban would have no deterrent effect and insisted she has no assets to freeze.
A statement issued through solicitor Aamer Anwar on their behalf said: "Aqsa's family described today's sanctions as little more than useless grandstanding by the Prime Minister which will have zero impact on the activities of Aqsa Mahmood, but more importantly do very little to deter young people from being recruited to Isis.
"The PM will know that Aqsa had no global assets to freeze and if he thinks that young people thinking of joining Isis will be worried about their pocket money being frozen in high street banks then he is sadly deluded.
"Aqsa's family remain full of rage at her activities, which they describe as a twisted and distorted perversion of Islam, but they had always hoped that one day she would see Isis for the barbaric death cult it is and return home.''
It added: "They appreciated that if Aqsa did, then she must face the full force of the law, but to impose a travel ban simply means that we are washing our hands of British citizens who want to break with Isis.
"They believe an imposition of a travel ban will have absolutely no deterrent effect on radicalised young Isis recruits, but the real danger is a future where some families will fail to inform the authorities when their children leave for Isis in case that door is closed for their return.
"The nightmare scenario for our security services is if those radicalised individuals return to this country, they will do so unmonitored and undetected. But it is also unacceptable that our Government is effectively absolving itself of any responsibility for British citizens by forcing those who wish to leave Isis to remain in Syria and carry on committing atrocities.''