Up to 5,000 Afghan refugees a day are crossing into neighbouring Iran, compounding the already heavy burden it faces hosting an estimated 3.6 million Afghans, a relief group said Wednesday.

The Norwegian Refugee Council called for more international support for Iran, which despite facing tough US economic sanctions, operates what the council described as one of the most inclusive refugee policies in the world. 

"Iran cannot be expected to host so many Afghans with so little support from the international community," the council's secretary general Jan Egeland said after a visit to Iran this week.

"There must be an immediate scale up of aid both inside Afghanistan and in neighbouring countries like Iran, before the deadly winter cold."

The council said it was estimated that at least 300,000 Afghans had crossed into Iran since the Taliban entered Kabul as US-led troops withdrew in August. 

"We've heard heartbreaking stories from families that have recently arrived in Iran," Egeland said.

"One refugee said they were targeted for being (Shiite) Muslim, their few remaining possessions were taken, their house burned and they had to flee multiple times within Afghanistan before reaching Iran."

The council said around $136 million of a $300 million appeal launched by the UN refugee agency to help up to 515,000 people who may flee Afghanistan before the end of the year was earmarked for Iran. 

It said so far the appeal was only 32 per cent funded.

"Now the international community must step up to support Afghanistan's neighbours and share the responsibility to help them to continue welcoming refugees," Egeland said.