The Kurdistan Region Security Council said on social media on Tuesday that its troops had liberated the girl near the Isis-occupied city of Mosul in northern Iraq on February 17th.
In a post published on Twitter, it wrote that it "was called upon by Swedish authorities and members of her family to assist in locating and rescuing" her from Isis.
However, the Swedish Foreign Ministry declined to comment when asked by Swedish media.
"We have no information to hand out about this case," spokesperson Katarina Byrenius Roslund told the TT newswire.
The Kurdistan Region Security Council said the girl, from the small town of Borås in south-western Sweden, had been "misled" by an Isis member in Sweden to first travel to Syria and then onwards to Mosul.
"She is currently in the Kurdistan Region and is provided the care afforded to her under international law. She will be transferred to Swedish authorities to return home once necessary arrangements are put place [sic]," it said.
A senior Kurdish security official told the AFP news agency on condition of anonymity that the operation had taken place in Mosul and had avoided any bloodshed.
"The operation was carried out secretly in the centre of Mosul... without clashes or the arrest of any gunmen," the official said.
"Swedish authorities were in continuous contact with the girl and organized the operation to rescue her in cooperation with regional authorities."
It is understood that the girl in question is the same then-pregnant teen who travelled with her 19-year-old boyfriend to the Middle East earlier this summer, where he was said to have joined an extremist group.
According to unconfirmed reports by Swedish tabloid Aftonbladet, the male teenager was later killed in a Russian air raid on the Iraqi city of Ramadi. It added that the girl gave birth to a son in November.
The circumstances of the rescue operation were unclear on Tuesday afternoon, but according to Swedish Radio, it followed another liberation attempt last year, which had initially been believed to be successful.
But Swedish journalist Kurdo Baksi, quoted by TT, said his contacts in the region had told him that the girl had then been kidnapped by other armed troops during the raid on an Isis camp last autumn.
"It's a group near Mosul which has specialized in murdering IS soldiers, but at the same time they carry out kidnappings and want paid," he said.
However, according to other, also unconfirmed report, the teenager had returned voluntarily to the same Isis troops that originally held her shortly after the first liberation attempt.
While much behind her journey to Syria and Iraq remains unclear, news of her situation follows a rise in young people making the journey from Scandinavia to the Middle East to join radical groups.
Sweden's Security Service, Säpo, does not comment on individual cases but has previously said that up to 300 Swedes are believed to have travelled to the region to fight in the past three years. Around 40 are thought to have died in battle and around 125 are understood to remain in Syria and Iraq – 90 men and 35 women.