Nato admitted that it had received credible reports that several civilians were killed in Panjwai but insisted that 48 Taliban fighters had died during the heavy fighting.
The operation had targeted Taliban who were attacking aid deliveries and reconstruction projects in the area, Major Luke Knittig, an International Security Force (Isaf) spokesman, said. Troops used "precision strikes" against Taliban, he added.
"Very sadly, civilians continue to get caught up in these engagements with tragic results," Knittig said.
After visiting the wounded in hospital, Naik Mohammad, a tribal elder, said that 60 civilians had died in the incident on Tuesday.
Villagers also put the death toll at 60 dead while a member of the Kandahar provincial assembly said that 80 had been killed.
Witnesses said that 25 homes had been destroyed in nearly five hours of bombing.
"It was late at night - that might be the reason they didn't know where to bomb," Agha Lalai, a member of the provincial assembly, said. "They have bombed residential houses."
"With insurgents who regard the population as a form of human shield for themselves it obviously makes life very difficult for us, but it does not stop us from making every effort to ensure that we minimise any problems".
Mark Laity, Nato spokesman
Another assembly member said civilian homes were targeted after Taliban fighters ran inside them.
"With insurgents who regard the population as a form of human shield for themselves, it obviously makes life very difficult for us, but it does not stop us from making every effort to ensure that we minimise any problems," said Mark Laity, a Nato spokesman.
"We know that the public rely on us and expect us to take every care, and if they [civilians] are accidentally killed then it can affect [public] faith in us," he added.
President Hamid Karzai has appointed a commission to investigate the attack after issuing a statement which said he was "deeply touched" by the reports.
The president "assigned an inquiry team to fully investigate the reports of civilian casualties during Nato's air operations in Panjwayi and Pashmul districts of Kandahar province," a statement said.
The United Nations mission in Afghanistan (UNAMA) on Thursday urged a speedy and thorough investigation.
"The United Nations Assistance Mission in Afghanistan is very concerned by reports that a great number of civilians may have died during the conduct of military operations," it said in a statement.
"The safety and welfare of civilians must always come first and any civilian casualties are unacceptable, without exception."
If confirmed, the bombings will have caused the highest number of civilian deaths by multi-national forces since the US-led invasion of Afghanistan after the September 11, 2001 attacks.
Karzai has repeatedly condemned civilian casualties, and last week urged Nato to take "maximum caution during military operations to avoid harming civilians".