The U.S. military would like to express its "deepest" condolences to the families of the victims, the statement said.
The incident occurred as us and Afghan forces returned from a joint operation, the Afghan source said.
Zabihullah Mujahid, Taliban spokesman, claimed four U.S. soldiers were killed in the attack.
A group of around 300 U.S. Marines arrived in the embattled province in April to support struggling Afghan forces in their battle against the Taliban.
The Taliban, in a statement, took credit for the attack, according to the SITE Intel Group.
This latest attack comes as the White House considers increasing those numbers again - discussions thought to center on an additional 3,000 to 5,000 U.S. and allied forces.
Three US soldiers were killed and another was wounded Saturday in eastern Afghanistan's eastern Nangarhar province, the Pentagon said.
On Friday two Afghan border police were killed by friendly fire - the first such incident since U.S. Marines returned to the country's southern region in May. The official asked not to be identified because the information had not yet been officially released and the USA military was still investigating the episode.
Achin district is in the Nangarhar province of Afghanistan, east of Kabul.
Sen. Cotton Rips Dems for Chasing 'Rabbit Trails' at Sessions Hearing
Attorney General Jeff Sessions hasn't sought any information on Russian interference in the 2016 presidential election, he said. Before he became attorney general, Sessions served two decades as a Republican senator from Alabama.
A White House spokesman said Trump was "following the emerging situation in Afghanistan" where the soldiers were killed.
Hoping to flush ISIS from its stronghold, American and Afghan forces launched Operation Hamza in early March. "The Afghan army soldier was killed in return fire".
Three U.S. Army soldiers were killed and another was wounded in an attack by an Afghan soldier for which the Taliban has claimed responsibility.
Also Known as the "green-on-blue" attack, the insider attack, where an Afghan government solider or police fires on North Atlantic Treaty Organisation coalition forces, is one of the major problems facing coalition forces there.
The latest killings come at a time of intensified violence and when the United States is considering sending more USA troops to Afghanistan.
She adds that shootings like the one that occurred Saturday "are called insider attacks - or green on blue - with Afghans wearing green shooting Americans and North Atlantic Treaty Organisation soldiers".
A United States warplane attacked a patrol of Afghan border police in the southern Helmand Province overnight, killing "several" and wounding a number of others.
Hundreds of US Marines recently arrived in Helmand to take over an advising mission as part of the NATO-led coalition training and assisting Afghan forces.
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