The blunder "adds to a sense of fear and insecurity" in the country, following similar killings of innocent civilians, the UN said.
UN special envoy Lakhdar Brahimi said in a statement that the protection of civilians was an "obligation" that any military had to uphold.
"The special representative and the United Nations family in Afghanistan have been profoundly distressed at the news that nine children were killed on Saturday in Ghazni as a result of coalition military action," said UN spokesman Manoel de Almeida e Silva, reading a statement from the envoy.
"This incident, which follows similar incidents, adds to a sense of insecurity and fear in the country," he said.
"We are aware that caution is taken but these kinds of mistakes... do have a negative impact among the population. We have seen this before so it's not as if were speaking without experience," de Almeida e Silva said.
In November, six civilians were killed in an air raid in southern Paktika province
Three weeks earlier, eight members of a family died in a similar attack in Nuristan
In July 2002, 48 people were killed and 117 injured in Uruzgan province when a US AC-130 gunship attacked a wedding party
The children died along with a suspected Taliban rebel in Ghazni province which has been troubled by attacks blamed on Taliban fighters.
"Following the attack, coalition ground forces searching the area found the bodies of both the intended target and those of nine children nearby," the US military said in a statement from the coalition's Bagram Air Base headquarters.
"Coalition forces regret the loss of any innocent life," the statement added.
Coalition aircraft had opened fire at about 06:00 GMT on Saturday in an isolated area south of the town of Ghazni, 130km southwest of Kabul.
The suspect was believed to be responsible for recently killing two contractors working on the Kabul-Kandahar-Herat ring road, the military said.
The US military said a commission of inquiry was being set up to probe the deaths, adding that its forces "follow stringent rules of engagement to specifically avoid this type of incident while continuing to target terrorists".
Meanwhile, Afghan police were hunting for suspected Taliban fighters who abducted two Indian road workers in Zabul province on Saturday.
The men were kidnapped after they had finished their day's work on the highway between Kabul and Kandahar, Zabul security commander Ayub Khan said.
"They (road workers)were not supposed to go out of the specified security area without guards and informing the security team"
Zabul security commander
Initial reports had said three workers were kidnapped, but the Indian embassy confirmed that two of its nationals had been seized.
Khan said two Afghans from Bazargan village working with the Indians had been arrested and were being investigated. "We don't know yet if they were involved in the incident or not," he said.
Khan said the Indians had gone to the village without first informing the authorities.
"They were not supposed to go out of the specified security area without guards and informing the road security team but the two Indians made the driver go to the villages without even informing road police and taking some guards," he said.