KABUL, Afghanistan (CNN) -- The U.S. military is investigating two airstrikes this week that Afghan officials say killed as many as 60 civilians.
Afghan President Hamid Karzai made an appeal to U.S. election winner Obama to "stop civilian casualties."
The latest incident happened Thursday morning in northwestern Afghanistan and left up to 30 civilians dead, according to officials in Badghis province.
The reported casualties come as the U.S. and NATO forces are waging a bloody battle against a resurgent Taliban across Afghanistan.
The incident also comes during the first visit to Afghanistan by Gen. David Petraeus as the top U.S. military commander in the region. Watch what Petraeus will tell Obama »
Afghan President Hamid Karzai said Wednesday that his "first and main demand" of the next U.S. administration under president-elect Barack Obama will be "to stop civilian casualties" in his country.
So far, Petraeus -- who took over as head of U.S. Central Command on October 31 -- has not publicly commented on the reported civilian deaths, a major source of tensions between the two countries in recent months.
Many Afghans accuse the United States of not taking caution when carrying out airstrikes in civilian areas and Karzai has been under enormous political pressure to stop the strikes.
Pakistan also complained Monday to Petraeus over American attacks against suspected terrorists inside Pakistan that have also left many civilians dead.
The U.S. military insists its forces "take extensive measures to avoid circumstances where non-combatant civilians are placed at risk."
Thursday's reported strike in Badghis province took place in the pre-dawn hours as coalition and Afghan soldiers battled Taliban forces near Afghanistan's border with Turkmenistan, according to the head of Badghis' provincial council and the province's deputy governor.
Between 20 and 30 civilians were killed and another 19 were wounded in an airstrike called in during the five-hour battle that ended at 9 a.m. local time Thursday (0430 GMT), the Afghan officials said.
The U.S. military said it was aware of possible civilian casualties and was investigating the incident jointly with NATO's International Security Forces (ISAF) and the Afghan government.
"If we find that innocent people were killed in this incident, we apologize and express our sincere condolences to the families and the people of Afghanistan," Col. Greg Julian, a spokesman for the U.S. forces in Afghanistan, said in a statement.
The statement said only that the incident may have happened Wednesday while coalition, NATO-led forces and Afghan National Security Forces were on a route-clearance patrol in the Ghormach district and responded to an insurgent ambush.
The U.S. military announced on Wednesday that it has launched an investigation into reports that a U.S. airstrike on Monday killed 35 civilians, including women and children, in Afghanistan's southern Kandahar province.
Taliban spokesman Qari Mohammad Yousif Ahmadi said the deaths happened after a firefight between Taliban forces and "enemy forces" from Monday to Wednesday. Thirteen soldiers and one Taliban fighter were killed, he said.
During the firefight, airstrikes were called in, leading to the 35 civilian deaths, he said. Fifteen civilians were also wounded, he said.
The U.S. military said Thursday that civilians attempted to leave during the battle in Shah Wali Kott, "but the insurgents forced them to remain as they continued to fire on the ANSF (Afghan National Security Forces) and Coalition forces along the highway."
Nine insurgents were killed and there were no Afghan or coalition casualties, according to the U.S. military.
The issue of civilian casualties has rankled relations between the United States and Afghanistan. After a U.S. airstrike in August that killed dozens of civilians in the western province of Herat, U.S. Defense Secretary Robert Gates traveled to Kabul to apologize to Karzai.
Afghan and United Nations officials said the airstrike killed 90 civilians. The U.S. military initially denied such a large number of civilians were killed. But when cell phone pictures were later provided to the U.S. military showing dozens of bodies at the scene of the strike, the top U.S. military commander in Afghanistan, Gen. David McKiernan, asked U.S. Central Command to review the initial investigation.
That investigation concluded that 33 civilians were killed.
Meanwhile, it was revealed that progress was being made in setting up the next round of talks between Afghan officials and the Taliban, a Saudi source told CNN Thursday.
Afghan President Hamid Karzai's brother, Qayum, recently met with Saudi officials to help organize the next round, the source said. Qayum Karzai is the Afghan coordinator for the discussion and is working on a list of names for the Saudis to invite to the talks.
In September, Saudi King Abdullah hosted talks between the Afghan government and the Taliban for four days in Mecca.
The Saudi source cannot be named because he is not allowed to talk on this subject. However, he has provided reliable information in the past.
CNN's Atia Abawi and Tamim Mayar in Kabul, Afghanistan contributed to this report.