A US commander on Wednesday apologised for leaflets dropped in Afghanistan that were deemed offensive to Islam.

A US commander apologised on Wednesday for leaflets dropped in Afghanistan that contained a quote from the holy Quran alongside an image of a dog.

The leaflets, which were dropped on Monday night encouraging Afghans to cooperate with security forces, were deemed "highly offensive".

They included an image of a dog carrying the Taliban flag, which included verses from the Quran inscribed.

"The design of the leaflets mistakenly contained an image highly offensive to both Muslims and the religion of Islam," Major General James Linder said in a statement.

"I sincerely apologize. We have the deepest respect for Islam and our Muslim partners worldwide," he said, adding that an investigation would be held "to determine the cause of this incident and to hold the responsible party accountable".

Dogs are regarded as unclean in much of the Muslim world.

The deputy governor of Parwan province Shah Wali Shahid said demonstrations were expected across the province.

"Local people are very upset with this incident, and they want the perpetrators brought to justice," Shahid said.

Throughout the 16-year Afghan war, US forces have struggled to convince ordinary Afghans to help them defeat the Taliban.

Monday's incident highlights one of the challenges that faces Western forces - consisting mostly of non-Muslims - in the deeply conservative country.

Anti-foreigner sentiments continue to be stoked by foreign forces stationed in Afghanistan through religious offences.

In 2012, copies of the Quran were mistakenly burned at the Bagram Air Base near Kabul, sparking mass demonstrations across the capital city and other provinces.

US commanders were forced to apologise over the incident.