The children, aged between one and eight, were left orphaned after their father was killed in battle in the Syrian town of Baghouz in March. Their mother was also killed in early 2019.
Their grandfather fought to return the children to Sweden after their parents' death, and after talks between the Swedish foreign ministry and the Kurdish al-Hol refugee camp in Syria, where the children stayed before being moved to Iraq, they arrived in Sweden on Wednesday.
Three of the children were born after Skråmo and their mother went to Syria to join militant Islamist group Isis, and the other four were born in Sweden. They were found ill and malnourished in the refugee camp when their grandfather managed to locate them.
“When we landed they yelled 'yay',” he told Swedish broadcaster SVT. “The journey went well and the children were calm.”
The seven children will now be brought under the care of the Gothenburg social services.
“We do not comment on individuals for reasons of confidentiality. But I can tell you what would generally happen,” social services spokesperson Ing-Marie Larsson told newswire TT.
“When you land without a legal guardian, and you tragically don't have any parents left, the social services then step in and launch an investigation into the needs of these children.”
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A person who will be legally responsible for ensuring the children are provided for will be appointed by a court, among other things.
“Meanwhile the children's needs for various assistance, such as health care, support calls if they are traumatized and so on, will be looked at,” said Larsson.
“We always have the children's best interests and their need for safety in mind.”
Around 60-80 children with a Swedish connection are believed to be held at the al-Hol refugee camp, with the question of how to solve the situation for children of Isis affiliates remaining highly debated.
Several parliamentary parties have criticized the Swedish government for not acting fast enough – something that has been rejected by Foreign Minister Margot Wallström.
“We work as fast as we can. But there is no quick fix for this as some seem to believe,” she said last month.
Since 2012, around 300 people have travelled from Sweden to Syria and Iraq to join violent Islamist groups in the region, mainly the terrorist organization Isis.
Roughly half of them have returned back to Sweden.
Skråmo, a Norwegian citizen born and brought up in the Swedish city of Gothenburg, was one of the most prolific propagandists of Isis.