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The deaths of Jasso and the three service members bring the number of US troops killed in Afghanistan this year up to 13. The four injured people were evacuated and are receiving medical care, military officials said.
No other details about the deadly incident were available.
Combined, the deaths bring the number of US troops killed in combat in Afghanistan this year to 13.
On Nov. 24, a U.S. soldier was killed "while conducting an operation to eliminate al Qaeda militants" in the southwestern province of Nimroz.
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He said US Special Forces had been conducting operations with Afghan forces around Ghazni city since Monday. The two districts, which are predominantly comprised of Hazara populations, were considered to be the most secure rural districts in all of the country.
The Taliban carry out near-daily attacks on Afghan forces, and in August the insurgents overran parts of Ghazni, leading to days of intense fighting before they were driven out.
Jasso was apparently hit "when the partnered force became engaged in a close-quarter battle during an assault on one of multiple barricaded al-Qaeda shooters". "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".
The US, alongside with North Atlantic Treaty Organisation has been present in Afghanistan in the form of the Resolute Support Mission.
Their deaths bring to 13 the number of U.S. troops killed in Afghanistan this year. Brent Taylor of the Utah National Guard was killed in an "insider attack" by a rogue Afghan commando he was training in Kabul. The U.S. military involvement began within weeks of the September 11, 2001, terror attacks.