Two of Afghan President Hamid Karzai’s brothers and several top security officials were in the delegation in Panjwai in Kandahar province.
One Afghan soldier was killed and three other people injured but the delegation is heading back to Kandahar city.
The US soldier said to have carried out Sunday’s attacks is under arrest.
The unnamed 38-year-old staff sergeant is being held at an undisclosed location.
A senior Afghan official confirmed that an attack “from several directions” had taken place on the delegation, which was there to meet villagers and tribal elders. Afghan forces returned fire.
Officials reported a 10-minute gun battle during which Taliban fighters fired from a distance at a mosque where the delegation and civilians were taking part in a prayer service.
One of Mr Karzai’s brothers, Qayum, told the Associated Press news agency it appeared initially that the attack was not serious and the delegation “assumed that it was the national army that started to fire in the air, according to BBC.
He said the delegation, which included Kandahar’s governor and the minister of border and tribal affairs, was safe and returning to Kandahar city.
The US soldier’s attack in Kandahar has severely strained relations between Afghans and foreign forces.
Anti-US sentiment was already high after soldiers burned some copies of the Koran at a Nato base in Kabul last month, sparking deadly riots across the country.
On Tuesday morning, some 600 students took part in a rally in the eastern city of Jalalabad, condemning the Kandahar attack and chanting “Death to America! Death to Obama!”.
US President Barack Obama said the shooting was “absolutely heartbreaking and tragic”.
But he said international forces must be withdrawn from Afghanistan in a responsible way, and would not “rush for the exits”.
He said the international forces had to make sure Afghans could secure their borders and stop al-Qaeda from getting back into the country.
US Defence Secretary Leon Panetta said the soldier in question could face the death penalty, if found guilty.
The Taliban has renewed threats of revenge attacks, saying it would behead “sadistic” American soldiers.
Details about Sunday’s shootings are still unclear, but the American soldier left his base in Kandahar in the early hours and went on a rampage in nearby villages.
Locals told reporters how they cowered in fear as the man made his way from door to door, trying to get into their houses.
“I saw a man, he dragged a woman by her hair and banged her head repeatedly against the wall. She didn’t say a word,” one witness said.
He broke into three houses and killed 16 people, most of them women and children. He then burned their bodies, according to reports.
The US defence secretary said the soldier “came back to the forward operating base and basically turned himself in, told individuals what had happened”.
Pentagon officials said they would not release his name while the investigation was going on.
Reports said the soldier, who has three children, had been deployed to Afghanistan in December for his first tour of duty there after serving three times in Iraq.