If the claims are verified, the deaths in Farah would be the largest loss of civilian life in a single incident since US-led forces invaded Afghanistan in 2001.
Hillary Clinton, the US secretary of state, said in Washington on Wednesday that the Obama administration "deeply, deeply" regrets the loss of innocent life, calling such incidents "particularly painful".
Hamid Karzai, Afghanistan's president, in the US capital for a US-Afghanistan-Pakistan meeting, thanked Clinton for "showing concern and regret" and said he hoped the two sides would work together completely to reduce civilian casualties in the "struggle against terrorism".
And Jim Jones, US national security adviser, said on Wednesday at a White House news briefing that investigations would be pursued "aggressively" to discover what had happened.
'Dozens of bodies'
Jessica Barry, a spokesperson for the International Committee of the Red Cross (ICRC), earlier said that the organisation sent a team to the region after concerned tribal leaders contacted them seeking help.
"When [our team] went to the first two villages where these incidents took place they saw dozens of bodies. They saw graves and they saw people being buried," she told Al Jazeera.
Barry said that an ICRC community-based first aid volunteer and his extended family, including his five daughters and three sons, were among the dead.
She said that they were killed while sheltering in their home.
The US said on Tuesday that it was conducting a joint inquiry, along with the Afghan government, into the deaths, with investigators from both sides visiting the sites.
Robert Wood, the acting US state department spokesman, said in a statement: "Coalition forces and the Afghan government have received reports of civilian casualties in conjunction with a militant attack on Afghan National Security Forces in Farah Province on May 5.
"A joint investigation will be conducted to determine exactly what happened."
Colonel Greg Julian, a US military spokesman, acknowledged that a battle had taken place, but could not say if there had been civilian deaths.
"Once we get eyes on the ground we will have a better idea of what may have happened," he said.
Account of clash
The deadly clashes in Bala Baluk occurred after Taliban fighters killed three former government officials in a village for co-operating with the state, Amin, the Farah governor, said.
He said that villagers had brought lorryloads of bodies to his office in the provincial capital as proof of their death.
If verified, the Farah deaths would be the largest loss of civilian life in a single incident
The US government has come under increasing criticism during the past year for civilian deaths during operations against Taliban and al-Qaeda fighters in Afghanistan.
Barry, the ICRC spokesperson, said: "I think that it is important to remember that this is not a one-off situation. There has been a rise in casualties over the last year.
"It is absolutely important to remind all sides that civilians must not be harmed."
For his part, Wood of the state department said: "US and international forces take extensive precautions to avoid loss of life among Afghan civilians as well as international and Afghan forces during operations against insurgents and terrorists."
Karzai said that the civilian deaths in Farah were unacceptable and that he intended to discuss it with Barack Obama, his US counterpart, on Wednesday.
The trilateral talks involving Karzai, Obama and Asif Ali Zardari, the Pakistan president, are aimed at addressing the war against the Taliban.
Focus on fighting
The Taliban has used Pakistan's border region with Afghanistan as a base to launch attacks in the two countries since their five-year rule in Kabul was ended by a US military invasion in 2001.
Washington has heightened its focus on fighting the Taliban since the Obama administration assumed power this year, with an added 21,000 troops being sent to Afghanistan.
There are more than 30,000 US troops in Afghanistan already, alongside a similar number of troops from other foreign nations.
Last year, about 2,000 civilians were killed in fighting against the Taliban, according to the UN.