The United Nations is investigating claims that up to 32 civilians were killed in a US airstrike in the volatile Afghan province of Kunduz last week, calling any loss of civilian life "unacceptable".

The strike early last Thursday triggered angry protests in Kunduz, with local officials saying at least 30 people had been killed, many of them children whose mutilated bodies were paraded through the streets by grieving relatives.

Civilian casualties caused by NATO forces have been one of the most contentious issues in the 15-year campaign against the insurgents, prompting strong public and government criticism.

US forces have conceded that the strike "very likely" resulted in civilian casualties and pledged a full investigation into the incident. A State Department spokesman called it a "terrible event".

The killings came just days before the US presidential election, in which Afghanistan has received scarcely a passing mention -- even though the situation there will be an urgent matter for the new president.

Either Donald Trump or Hillary Clinton will inherit America's longest war with no end in sight.

It was also the second time in just over a year that a US airstrike has gone wrong in Kunduz.

Last year, a US air strike during fighting hit a hospital operated by Medecins Sans Frontieres on October 3, killing 42 people and sparking international outrage.

Late Sunday the UN's mission in Afghanistan (UNAMA) announced it is investigating the allegations surrounding Thursday's strike.

"Preliminary findings indicate that the aerial operation killed at least 32 civilians and injured an additional 19 civilians, the vast majority of whom were women and children," a UNAMA statement said.

"The loss of civilian life is unacceptable and undermines efforts toward building peace and stability in Afghanistan," said Tadamichi Yamamoto, the UN special envoy to Afghanistan.

"When conducting aerial operations, international military forces should take all feasible measures to minimize civilian harm, including full analysis of the context for aerial strikes."

Thursday's strike came after a Taliban assault left two American soldiers and three Afghan special forces soldiers dead in the Boz-e-Kandahari area near the provincial capital.

Errant air strikes contributed to a 42 percent jump this year in casualties caused by pro-government forces compared to last year, according to the UN.