Some of al-Shabaab's top leaders have been killed in USA drone strikes, but its operations have continued in Somalia despite the resistance.
The attack by suspected Al-Shabaab militants occurred on Friday in Somalia's southern Jubaland province, where a small joint US-Somali outpost came under small arms and mortar fire, US defense officials said.
Somali officials have said civilians have been killed in more than one joint USA military operation with Somali forces.
Friday's attack also follows the October 4 ambush in Niger that killed four USA soldiers, their interpreter, and four Nigerien troops.
The coalition force was conducting a "multi-day operation" to clear al-Shabaab, an Islamist militant group, from nearby villages.
Al Jazeera's Rosiland Jordan, reporting from Washington, DC, said about 500 USA troops are deployed in Somalia, including highly-trained special forces and Navy Seals.
President Donald J. Trump issued his condolences to the American soldier who lost his life on Friday.
Although one of the wounded Americans did not receive additional care after being treated in the field, the other three and the wounded local soldier were medically evacuated for follow-up care.
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Hundreds of newly trained al-Shabab fighters perform military exercises in the Lafofe area south of Mogadishu, Somalia, on February 17, 2011. Though the Pentagon initially described Miliken as operating behind Somali troops, US officials later acknowledged that USA special operations soldiers had been fighting together with the Somali forces.
The statement said the mission's objectives were to clear al-Shabaab from contested areas, liberate villages from al-Shabaab control, and establish a permanent outposts created to increase the span of Federal Government of Somalia security and governance.
The U.S. military and others have expressed concern about the 21,000-strong AU force's plan to withdraw by 2020 and hand over security responsibilities to Somali forces, saying the local troops are not ready.
The injured service members were taken to Djibouti, where US Africa Command (AFRICOM) has its amp Lemonnier base.
The names of victims will not be released until the families have been notified.
The October attack in Niger raised questions in Washington about the USA military presence across Africa as the Trump administration focuses counterterror efforts on a range of groups linked to al-Qaida and the Islamic State group.
Mostly composed of special operators such as Army Green Berets, Navy SEALs and Marine Raiders, the United States forces in Somalia have conducted frequent raids and drone strikes on Shabaab training camps throughout Somalia.