"Words alone cannot begin to express our regret and sympathy and we will ensure the surviving family members are properly cared for," Ryan said.
Al Jazeera's Todd Baer, reporting from Kabul, said that while the US operation was going on, the family thought that somebody had entered their home unlawfully to steal.
"They began shooting at soldiers. So the soldiers returned fire," he said.
"There has been enormous pressure from citizens on the Afghan government to end these kinds of civilian casualties, end these kind of raids on houses."
Colonel Graig Julian, a US officer, told Al Jazeera: "When it appears that we have accidentally killed innocent civilians, we are very sorry about that. That is not why we came here. We came here to provide security for the Afghan citizens."
Violence in Afghanistan has reached its highest level since the US-led invasion to overthrow the Taliban government in 2001, despite a growing number of foreign troops.
In the latest clashes, Afghan and US-led multinational forces said they killed 27 fighters in two separate battles in the southern provinces of Helmand and Uruzgan on Friday.
A spokesman for Helmand's governor said the toll could be higher, with up to 36 people killed and 18 others wounded in one battle.
In a second incident in Helmand, six police officers were killed and seven wounded by suspected Taliban fighters in Nava district.
Barack Obama, the US president, wants to increase troop numbers further and is seeking the support of Nato countries, also stationed in Afghanistan, for a "surge" strategy similar to that operated in Iraq.
However, forces opposed to the US-backed Afghan government have been able to take the conflict from their strongholds in the south and east to the outskirts of the capital, Kabul.
Hundreds of civilians have been killed in operations by Afghan and foreign forces, an issue that has angered residents and increased pressure on Hamid Karzai, the country's president.
The casualties have also been a major source of friction between the Afghan government and the West.