The American was killed when a NATO coalition base in the capital city, Kabul, was attacked, a defense official told CNN. Another official told CNN's Barbara Starr that nearly 20 people of varying nationalities were wounded.
Separately, U.S. Army Col. Brian Triebus said in a statement that eight Afghan civilian contractors and four insurgents were also killed in that incident. Triebus also said a coalition service member was killed, but he did not give the nationality of that person.
There are approximately 9,800 U.S. troops in Afghanistan.
Taliban spokesman Zabiullah Mujahid said the group was responsible for the attack on the NATO base and for a suicide bombing at that took place at the National Police Academy earlier in the day.
The suicide bomber ignited his explosives at the police academy's front gate at around 7 p.m. local time, according to Ebadullah Karimi, a spokesman for the Kabul Police Chief. That's where students had queued to enter the training facility, said an Afghan police official in the police hospital who didn't want to be named.
Authorities said 27 students were killed and 26 people were wounded in that attack.
The incidents at Camp Integrity and the National Police Academy came hours after another explosion in Kabul.
At around 1 a.m. local time, a truck detonated on a main road, killing 15 people and wounding 240, said Sayed Zafar Hashemi, a deputy spokesman for President Ashraf Ghani.
The ensuing explosion destroyed residential areas and businesses, Police Chief Abdul Rahman Rahimi said.
Among those injured were 47 women and 30 children, Hashemi said.
Authorities were investigating the truck blast. There were no claims of responsibility late Friday.
From January 1 to Friday, 282 people have been killed and 1,241 have been injured in attacks launched by "anti-government elements" in Afghanistan, according to the United Nations Assistance Mission in Afghanistan (UNAMA). The UNAMA says that's nearly double the amount of death and injuries compared to the same period last year.
The U.S. State Department and UNAMA Saturday condemned the attacks.
National Security Adviser Susan Rice called President Ghani on Saturday to "express the deepest condolences of the American people" on Afghan deaths in the attacks, and Ghani in turn extended condolences for the U.S. service member's death, according to a statement from the White House.
Taliban's new leadership
The attacks come just days after the Taliban announced the death of the man who is credited with creating the group, Mullah Mohammed Omar
, and named his replacement, Mullah Akhtar Mohammad Mansour.
His death has thrown the already-fragile peace talks between the Sunni Islamists and the Afghan government into flux; a second round of talks was slated to take place in Islamabad on July 31 but was postponed after the Taliban confirmed Omar's death.
One analyst told CNN that Mansour's rise may bode poorly for the peace talks.
"People should perhaps reassess the line which has been put about that he was leading the movement towards peace," Michael Semple, a professor at the Institute for the Study of Conflict Transformation and Social Justice at Queens University Belfast, told CNN
. "He is the one who has presided over the movement during a period of escalation of the violence. Actions speak louder than words."
Semple's assertion appears to be backed up by an audio tape that was recently released and purports to be from Mansour.
In the message, the Taliban's new leader denied that the group is attempting to work toward a peace process.
"When we hear about different processes including the peace process, they are all the propaganda campaigns by the enemy," the message says. "They are spreading their propaganda by spending money, through media and some scholars to only weaken our jihad, but we will not pay attention to any of those including the peace process. We will continue our jihad and we will fight until we bring an Islamic rule in the country."