The White House said Army Reserve Major General Rick Waddell provided updates.
Vice President Pence addressed the attack in his remarks at an event in Wisconsin on repealing Obamacare. "But suffice to say, when heroes fall, American grieve and our thoughts and prayers are with the families of these American heroes", Pence stated.
The incident took place in the restive Achin district of the eastern Nangarhar province where the US and the Afghan forces were conducting an operation against the Daesh terrorists. The soldiers' identities weren't immediately available nor were their military branch.
He said the Afghan soldier was killed in the incident on Saturday.
"Green on blue" violence, or insider attacks by Afghan soldiers on USA or other foreign troops, have become rare as coalition forces have mostly withdrawn from Afghanistan.
Such strikes have bred deep mistrust between local and foreign forces.
North Atlantic Treaty Organisation troops have adopted special security measures in recent years to try to counter the threat.
The policemen were on patrol too close to a Taliban base ahead of the attack, Afghan officials told AFP.
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Three US troops were killed and another wounded during a joint operation in Afghanistan's eastern Nangarhar province on Saturday (Jun 10), the Pentagon said, in the latest so-called insider attack on worldwide forces. This incident is under investigation.
"We can confirm personnel from the Afghan National Defence and Security Forces were killed and wounded during overnight operations in Helmand province".
Local media reported at least two deaths, while the Reuters news agency quoted Omar Zwak, a spokesman for the Helmand governor, as saying that three officers had lost their lives and two were wounded.
Taliban forces have gained a large amount of territory across the Helmand Province, including parts of the capital city of Lashkar Gah.
NPR's Amy Held notes that while the US officially withdrew from Afghanistan in 2014, roughly 8,400 troops remain in the country - and the Trump administration has been considering requests to increase those troop levels.
American troops, including special forces, also carry out separate counterterrorism missions.
It also comes as the Taliban ramp up their campaign against the Western-backed government in Afghanistan, and as US President Donald Trump mulls sending more troops into the lengthy conflict.
The three previous USA soldiers deaths in Achin make up the entirety of US combat fatalities in Afghanistan in 2017.