Dozens of people were killed and wounded in fighting at the airport in the southern Afghan city of Kandahar after an overnight attack by Taliban insurgents that security forces had not entirely suppressed nearly 24 hours later.

With final mopping up operations continuing late on Wednesday afternoon, at least 37 civilians and members of Afghan security forces had been killed and 35 wounded, the defence ministry said.

In addition, nine Taliban were killed and another wounded with a final survivor still resisting security forces, the ministry said in a statement, adding that the operation had proceeded slowly to minimise casualties.

"Afghanistan's national army forces are bravely fighting terrorists in airport areas and are trying to act cautiously to avoid harm to civilians," the ministry said.

The airport in Kandahar, Afghanistan's second biggest city, has for years been a major hub for operations of international forces, most of whom had withdrawn from Afghanistan by the end of 2014.

A spokesman for NATO's Resolute Support mission said there had been no reports of casualties among the hundreds of international personnel at the air base but he had no other details.

The raid in one of the Taliban's traditional strongholds coincided with the start of the Heart of Asia regional security conference in Islamabad, where Afghan President Ashraf Ghani made a plea for more regional support to fight the growing Islamist insurgency.

Officials said fighters attacked a perimeter area of the huge and heavily fortified complex on Tuesday evening, initially taking up position in a school in a residential area of the site, which houses both a civilian airport and military base.

NATO military personnel, civilian contractors and Afghan forces are based there.

Earlier, the Taliban said in a statement 150 soldiers had been killed but the militants often made exaggerated casualty claims in the past.

The Taliban, fighting to re-establish hard-line Islamist rule after US-led military intervention toppled their regime in 2001, have been struggling to settle a leadership dispute which has seen scores killed in fighting between factions.

But the attack on one of the most heavily protected bases in the country underlined their ability to inflict serious damage on security forces still shaken by the Taliban's brief capture of the northern city of Kunduz in September.

The Taliban said suicide attackers had entered the base and attacked international forces and their Afghan allies.

The attack follows an earlier incident in which two suicide bombers died attacking a police station in Kandahar.