Asylum seekers in Norway are being offered cash and free flights to leave the country as it struggles to cope with the worsening migrant crisis rooted mostly from the four-year civil war in Syria.

Close to a thousand people have accepted the offer, which allows a family with two children to apply for up to $9,300 in cash aid plus free flights home, the Norwegian immigration office said.

"[Refugees] thought that when they came to Norway they would get protection rather quickly. Instead, applications for family reunification can often take years, and an increasing number of refugees fleeing conflict in the Middle East and Africa don't want to wait,'' Katinka Hartmann, head of the immigration department's unit said, Fox News reported.

She told Norwegian news outlet NRK: "They thought they would have the opportunity to work or take an education, and maybe even to get their family to Norway. Many cannot wait. They have a family at home who expect them to be able to help.''

Another consideration that has been discouraging refugees from staying is the housing problem in the Scandinavian country. Many reportedly found themselves taken to remote communities where work is difficult to find.

Joo van der Aalst, spokesman for the International Organisation for Migration (IOM), which processes the return programme, told NRK that the number of asylum seekers taking up the offer was ballooning.

"Earlier this year, the number [of applications] was an average of 100 per month. In October, there were 150 and in November there were 230 applications," he said.

He said refugees whose asylum applications have been denied are also allowed to apply for financial assistance to return home.

The IOM said the Voluntary Assisted Return Programme is "organised, safe and dignified.''

The Norwegian immigration office said the amount of economic support to asylum seekers may be reduced in the future.