As her family pleaded for the teenager to be allowed back to Britain "as a matter of urgency", the 19-year-old who is nine months pregnant said she understood the controversy and intense media scrutiny a return to the UK would bring.
But said she did not want to be separated from her child.
"I don’t want it to be taken away from me, or at least if it is, to be given to my family," she told The Times.
They said the pregnant 19-year-old and her unborn child should be allowed to return home to Bethnal Green and be “dealt with under the British justice system”.
Their plea came Britain's counter-terrorism chief Neil Basu warned that any British nationals returning from Syria could expect to be investigated and would have to live under stringent limitations.
He said anyone returning from the war-torn country would be assessed to determine whether they had committed “any terrorist or other criminal offences”.
Ms Begum’s family said they were prepared for the teenager – currently in a camp where almost 40,000 Isis fighters’ family members are being held – to face questioning by the British authorities.
“We welcome an investigation in what she did while she was there under the principles of British justice and would request the British government assist us in returning Shamima and her child to the UK as a matter of urgency,” the family told ITV News. “As a British citizen, Shamima has every expectation to be returned to the UK and be dealt with under the British justice system.
“Shamima’s child who will also be British has every right as a total innocent to have the chance to grow up in the peace and security of this home.”
Ms Begum, who left London in 2015 with two friends, is currently living in at a refugee camp in northern Syria.
She told The Times earlier this week that she would “do anything required just to be able to come home and live quietly with my child”.
Her case has received high-profile backing, with former MI6 chief Richard Barrett saying the teenager should be given a chance to return “if we are to stand by our values”.
But the government has indicated it will not be contacting local authorities to negotiate her passage out of a camp.
Home Secretary Sajid Javid warned he “will not hesitate” to prevent the return of Britons who travelled to join Isis, while security minister Ben Wallace said he would “not put British lives at risk” to help Ms Begum.
Mr Basu, appointed national counter-terrorism chief last year, explained what was likely to happen to any UK nationals returning from Syria or Iraq if they had gone in support of any proscribed terrorist group.
“Any investigation is carried out with an open mind and based on the evidence available,” he said. “This is to determine if individuals have committed any terrorist or other criminal offences, regardless their motivation, and to ensure that they do not pose a danger to the public or the UK’s national security.
“There can be no hope of repatriation without these investigations taking place, and anyone who does return to the UK from conflict zones can, at best, expect to live under stringent limitations set out in the Terrorism Prevention and Investigation Measures (TPIM) Act.”
The former independent reviewer of terrorism legislation Lord Carlile has argued that if Ms Begum has not gained a second citizenship of another country, she will have to be allowed to return because under international law it is not possible for a person to be made “stateless”.
Mr Barrett, a former director of global counter-terrorism at MI6, suggested it would be “unreasonable” to expect the Syrian Defence Force to look after her indefinitely at the detainee camp.