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One American contractor was also wounded. The survivors were evacuated from the area and are receiving medical attention.
Taliban militants claimed responsibility for the attack in the city of Ghazni, where USA forces have waged fierce battles against the Taliban for months.
He said US Special Forces had been conducting operations with Afghan forces around Ghazni city since Monday.
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The US already has a $10 million bounty offered for Saeed and $2 million for Hafiz Abdul Rahman Makki, another senior group leader.
US military officials said the attack Tuesday took place during a military patrol near Ghazni city, which has remained tense and unstable since Taliban forces overran it in August in a four-day siege that left more than 100 people dead and parts of the city in ruins.
The names of those killed were not immediately disclosed pending the notification of next of kin.
Indiscriminate assaults by the Taliban and fighters from the Khorasan Province branch of the Islamic State of Iraq and the Levant (Isil) have left millions of Afghans fearing for their lives each and every day. "All of us, and through our coalition of 41 nations, recognize the threats posed by groups such as al-Qaeda and ISIS and are determined to fight them here".
Their deaths bring to 13 the number of U.S. troops killed in Afghanistan this year.
Global forces have also suffered from so-called insider attacks in recent months, in which Afghan soldiers or police have opened fire on them.
Resolute Support said upon further investigation, it appears Jasso was "accidentally shot by our Afghan partner force".