The SDF, the rebel group backed by the USA that controls the camp where Ms Begum, 19, is living, had earlier insisted that the baby was alive after a lawyer for Ms Begum's family, Tasnime Akunjee, tweeted that he had "strong but unconfirmed reports" that Jarrah had died.
Javid previously confirmed the baby was a British citizen and said he had considered the child's interest when deciding to revoke Begum's citizenship.
The U.K. stripped Begum of her citizenship under the British Nationality Act, but Home Secretary Sajid Javid said the decision wouldn't have applied to Jarrah.
Their lawyer Aamar Anwar told the Sunday Mirror: "If it was your daughter would you not want her back?"
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She hit the headlines again last month when she was found in a refugee camp in Syria and gave exclusive interviews to the press, asking to return home.
Begum also told reporters she had lost two other children.
Asked whether there was any plan for Ms Begum's son, Mr Javid told the Commons Home Affairs Committee it would be "incredibly difficult" for the Government to facilitate the return of a child from Syria.
Begum's family is challenging the U.K.'s decision to revoke her citizenship. But he later deleted the tweet without explanation, and shortly after confirmed the baby's death.
He added: "I have nothing but sympathy for the children that have been dragged into this".
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The baby, however, retained his citizenship and could have been allowed into the UK. CNN has contacted the UK Foreign and Commonwealth Office for comment, but has not yet received a reply.
"My number one job is to do whatever I can to keep this country safe", Mr Javid had said last month when announcing the revocation of citizenship.
It told them that the possibility of bringing the baby to the United Kingdom was a matter for the Foreign and Commonwealth Office and that they would need permission from Ms Begum.
Her husband, Dutch IS fighter Yago Riedijk, admitted they had both made a mistake when they joined the terror group.
The FRO is obliged to consider requests for consular assistance, the letter added.
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