An Australian father's speedy rescue of his two kidnapped sons has embarrassed Swedish police, who struggled with the case for six months.

Armed with just a pair of binoculars and a rental car, it took the unidentified man only one week to find his missing sons, aged 11 and 10, in Sweden.

"It is a genuine failing mark to the work of the police," columnist Lars Lindstrom wrote in the Swedish newspaper Expressen.

"(The father) went on leave, flew from Melbourne to Sweden and found them in a week. How did that happen?"

The boys were allegedly abducted in October last year by their Swedish mother.

She was charged with their kidnapping and became a wanted fugitive in Sweden.

The father had custody of the children but the mother was granted access twice a year.

After six months of waiting at home in Melbourne for a break in the case, the dad decided to take matters into his own hands.

He flew to Sweden, rented a car and parked outside the home of the mother's parents, on a hunch that they were harboring the fugitive mother and the children.

After a week of waiting, he crept out of his car under the cover of night and walked towards the front door.

For the first time in six months, he heard the sounds of his sons' voices coming from inside the building.

"I didn't even know the children were alive. The feeling was incredible,'' the father told Expressen.

He then went back to his car and called the Swedish authorities, who entered the home, arrested the mother and reunited the boys with their father.

The local authorities said they had done their best to find the children during the six month investigation.

"We have looked at a number of addresses,'' said Svante Melin, Detective Superintendent of Sodermanland Police in Sweden.

Swedish police had earlier suggested a feminist group had helped the mother with the abduction.

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