The family of Shamima Begum, who has left Britain to join the Islamic States group in Syria, told the Home Secretary that she would challenge his decision to revoke her British citizenship.
The letter to the BBC, Sajid Javid, says they can "not just give them up" and their status is "a matter of our British courts".
They added that they were "sick of the comments they made recently."
They also asked for support to bring their newborn baby to the UK.
Ms. Begum, who left Bethnal Green in east London in 2015, lives in a refugee camp in northern Syria and gave birth to a son last weekend.
In an interview with the BBC on Monday, she said she regrets not traveling to Syria, although she added that she disapproved of what the IS group did.
She told the BBC that she was "shocked" by the 2017 Manchester Arena attack that killed 22 people and called for IS. However, she also compared them to military attacks on IS strongholds of coalition forces.
The letter written by her sister Renu Begum on behalf of the family states, "We want to make it clear that we are shocked with the rest of the country and appalled at the vile comments she has recently made in the media ,
"These are not representative of British values, and my family completely rejects their comments."
Renu Begum says the family has made "every inscrutable effort" to prevent Shamima Begum from invading Islamic territory in 2015.
"This year, we lost Shamima to a murderous and misogynist cult.
"My sister has been spellbound for four years, and I realize that her exploitation on her hands has fundamentally damaged her."
From correspondent Daniel Sandford
Renu Begum's letter shows that Shamima Begum's family, which has been out of the limelight most of the week, is now ready to take over the Home Secretary in court and in the media.
She carefully emphasizes how shocked she was by Shamima Begum's comments.
However, she is equally vehement about how she can not give up her sister and how she "has to" – to use her words – question his decision.
The call for help to bring Shamima Begum's son back to Britain will be one of the most difficult parts of the letter for Home Secretary Sajid Javid.
He said in the House of Commons that the children of IS members would not lose their British citizenship.
Renu Begum points out that Jarrar, less than a week old, is the "only true innocent" in what they call "debacle."
In the letter, Renu Begum says that no family came in contact with Shamima, but they saw her "setting the emotions of our nation on fire" on television.
She says she was "sick" from Shamima's remarks, but he hopes Mr. Javid understands that her family "can not just leave her".
The letter states: "We have a duty to her and must hope that while she has become what she has become, she can also return to the sister I knew and the daughter, my parents gave birth.
"We hope that you understand our position in this regard and why we must therefore support Shamima in questioning her decision, the only thing her only hope for rehabilitation, her British citizenship, is."
The Ministry of the Interior has said that it is possible to deprive the teenager of British nationality on the grounds that he is entitled to the citizenship of another country – Bangladesh – through his mother, who is a Bangladeshi citizen.
- What legal status does Shamima Begum have?
- Why countries are in a dilemma about IS children
However, the Ministry of Foreign Affairs of Bangladesh has stated that Ms. Begum is not a Bangladeshi citizen and that there is "no question" of her admission into the country.
The Home Secretary said he would not leave stateless persons, which is illegal under international law.
Mr. Javid also suggested that Mrs. Begum's child could still be British despite the removal of Mrs. Begum's citizenship.
The leader of the Labor Party, Jeremy Corbyn, said that Javid had made an "extreme" decision and that she had "a right to return to the UK".
Geoffrey Robertson, QC, a former United Nations judge, said it was up to the British courts to set the punishment for joining a terrorist group.
He told the BBC, "It's certainly for a judge to decide whether to mercy or sympathy, not for a politician."