Two Dutch children have been abducted by their mother and taken to the ISIL-held city of Raqqa in Syria, the Dutch prosecution's office has confirmed.

The children's 32-year-old mother took the boy and girl, aged 7 and 8, from their hometown of Maastricht in southern Netherlands in October, after which Dutch police rang a major alert, public broadcaster NOS reported on Monday.

Despite an international arrest warrant, the woman, who is a Chechen national, managed to reach Syrian territory controlled by the Islamic State of Iraq and the Levant group (ISIL).

Her other two children were placed with a relative in the Netherlands, Dutch media reported.

After their arrival in Syria, the woman announced via Facebook that she and her children were in Raqqa. Nothing has been heard from them since, prosecutors told Dutch media.

According to the prosecutor's office, the woman had arranged for false passports for her and her children.

The prosecutor's office said it was the first time that Dutch children were abducted to ISIL-held territory.

The Dutch father of the children, Luca and Aysha, told newspaper De Limburger (Dutch) that they were taken by his ex-wife without his consent.

The man had previously gone to the police because he suspected that his ex was about to travel to Syria.

Police interrogated her several times, but she denied the alleged travel plans and no concrete steps were taken.

Prosecutor Bart den Hartigh told NOS that it would be impossible to recover the children, partly because the Netherlands has no legal relationship with Syria and that the woman and children were in a war zone.