Ms Begum 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.
Speaking to The Times at a refugee camp in northern Syria, she said: “What do you think will happen to my child?
“Because I don’t want it to be taken away from me, or at least if it is, to be given to my family.”
She also said she had been taken to hospital after having contractions following her arrival at the refugee camp, and could give birth “any day”.
The pregnant 19-year-old was tracked down by the newspaper four years after she travelled to Syria as a 15-year-old to join Islamic State, and she told how she would “do anything required just to be able to come home and live quietly with my child”.
Her case has been the subject of intense debate over what should happen to the teenager.
In a statement issued by their lawyer, her family urged the Government to help her return to Britain to protect the welfare of her baby.
“Given Shamima’s four-year ordeal, we are concerned that her mental health has been affected by everything that she has seen and endured,” they said.
“Now, we are faced with the situation of knowing that Shamima’s two young children have died - children that we will never come to know as a family.
“This is the hardest of news to bear.
“The welfare of Shamima’s unborn baby is of paramount concern to our family, and we will do everything within our power to protect that baby who is entirely blameless in these events.”
Ms Begum told The Times she understood she could face a police investigation on her return, admitting: “I knew that coming back to the UK wouldn’t be a quiet thing. It’s uncomfortable.
“If I ever do go back, it’ll be a long time before the cameras stop and all the questions stop.”
The former east London schoolgirl had previously admitted that she did not regret travelling to IS-controlled Syria, and asserted she was “not the same silly little 15-year-old schoolgirl who ran away from Bethnal Green four years ago”.
The statement her family issued on Friday evening said they were shocked by her comments in the interview, but her words were those “of a girl who was groomed”.
“We are also mindful that Shamima is currently in a camp surrounded by IS sympathisers and any comments by her could lead directly to danger to her and her child,” they added.
Her family said her unborn child had “every right as a total innocent to have the chance to grow up in the peace and security of this home”.
“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 statement said.
Meanwhile, the head of MI6 warned that Britons returning from Islamic State were likely to have acquired “potentially very dangerous” skills and connections.
Alex Younger, who did not comment specifically on the case of Ms Begum, said UK nationals have a “right” to come home but that public safety was the first priority.
Home Secretary Sajid Javid warned he would “not hesitate” to prevent the return of Britons who travelled to join IS, while security minister Ben Wallace said runaways who now wanted to come back must realise that “actions have consequences”.
The head of Counter Terrorism Policing, Assistant Commissioner Neil Basu, said anyone returning from a conflict zone having gone to support a terrorist group should expect to face a police investigation.
“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.”
Any hopes of a rescue mission by British officials were also swiftly quashed on Thursday as the Government ruled out an effort inside Syria to assist Ms Begum.
While refusing to comment on individual cases, Mr Wallace told the BBC: “I’m not putting at risk British people’s lives to go and look for terrorists or former terrorists in a failed state.
“There’s consular services elsewhere in the region and the strong message this Government has given for many years is that actions have consequences.”
Questions have been raised over whether Britain would be able to prevent Ms Begum’s eventual return to the UK.
Former independent reviewer of terrorism legislation Lord Carlile told the BBC that if Ms Begum has not gained a second citizenship of another country, she will have to be allowed back to her homeland because under international law it is not possible for a person to be made “stateless”.
Meanwhile, Richard 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.
He also warned that summary execution is the “most likely outcome” for such captured foreign nationals who are handed over to Syrian or Iraqi authorities.
Ms Begum was one of three schoolgirls, along with Kadiza Sultana and Amira Abase, from Bethnal Green Academy who left the UK in February 2015.
Another girl, Sharmeena Begum, also from Bethnal Green but not related to Shamima, had travelled to Syria two months earlier.
Ms Sultana was reported to have been killed in an air strike in 2016.
Shamima Begum said she had recently heard second-hand that the other two girls may still be alive.