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The Danish Refugee Council said Saturday its office in the southern Iraqi city of Basra had come under "armed attack" after a Copenhagen protest in which the Quran was believed to have been desecrated.

"Our staff on the premises at the time were physically unharmed, but there has been damage to the property with structures set on fire," the organisation's executive director for the Middle East, Lilu Thapa, said.

The early morning attack came amid protests in the capital Baghdad over an apparent desecration of the Muslim holy book during a small demonstration in the Danish capital that followed similar actions in Stockholm.

"We deplore this attack - aid workers should never be a target of violence," Thapa said.

"DRC has been working in Iraq for 20 years, providing support to communities affected by conflict and displacement, including demining operations across Basra."

The extreme right Danish group Danske Patrioter had on Friday posted on Facebook a video of a man burning what seemed to be a Quran and trampling an Iraqi flag.

Copenhagen police deputy chief Trine Fisker told AFP that "not more than a handful" of protesters had gathered Friday across from the Iraqi embassy.

Hundreds of protesters gathered in the Iraqi capital in the early hours of Saturday, seeking to march on the Danish embassy, an AFP photographer reported.