Asked if the attack was carried out by Nato forces, Omar said: "We will need to wait until we have a final report before we have the source as to what happened and who did it."
Karzai has ordered the National Security Council to investigate the incident, Sediq Sediqqi, head of media relations at the presidency, said earlier.
Reports surfaced on Saturday that a helicopter gunship fired on villagers who had been told by fighters to leave their homes as a firefight with troops from Nato's International Security Assistance Force (Isaf) was imminent.
According to witness accounts, men, women and children fled to Regey village and were fired on from helicopter gunships as they took cover.
Abdul Ghafar, 45, told AFP, a French press agency, that he lost "two daughters and one son and two sisters" in the attack.
He and six other families fled to Regey, about 500 metres from their village of Ishaqzai, after being warned about the imminent battle, he said.
Men and women took shelter in separate compounds, he said, ahead of an expected firefight between Taliban fighers and Nato troops.
"Helicopters started firing on the compound killing almost everyone inside," he said, speaking at the Mirwais hospital in Kandahar city.
"We rushed to the house and there were eight children wounded and around 40 to 50 others killed.".
Ghafar said he took three girls and four boys to the Kandahar hospital.
He said: "Three of the wounded are my nephews and one is my son.
"One of the wounded children is four years old and has lost both parents."
The BBC said it sent an Afghan reporter to Regey to interview residents, who described the attack and said they had buried 39 people.
Civilian casualties are an incendiary topic in Afghanistan, though surveys have shown that most are caused by Taliban attacks.
Colonel Wayne Shanks, an Isaf spokesman, said the location of the reported deaths was "several kilometres away from where we had engaged enemy fighters".
Isaf forces had fought a battle with the Taliban, Shanks said, but an investigation team dispatched after the casualty reports emerged "had accounted for all the rounds that were shot at the enemy".
"We found no evidence of civilian casualties," he said.
Leaked documents carried by Wikileaks, a whistleblower website, on Sunday pointed to under-reporting of civilian casualties, which Omar said were a cause of concern for the Afghan government.
The Pentagon files and field reports, spanning the period from January 2004 to December 2009, detail hundreds of unreported civilian deaths caused by Nato and Taliban attacks.
"We have continuously stated that the Afghan government and Afghan people were upset about civilian casualties," Omar told reporters, adding that Karzai had found nothing new in the leaked documents.
The White House condemned the leaks, saying the information could endanger US lives but also pointed to the administration's long-held concerns about alleged links between Pakistani intelligence agents and Afghan insurgents.