"Our thoughts and prayers are with the families and friends of our teammates who lost their lives today," U.S. Army Gen. Stephen Townsend, commander of U.S. Africa Command, said in a statement Sunday afternoon. "As we honor their sacrifice, let's also harden our resolve. Alongside our African and international partners, we will pursue those responsible for this attack and al-Shabaab who seeks to harm Americans and U.S. interests."
Two DOD employees were also wounded in the attack. They were listed in stable condition and were being evacuated, according to the Sunday statement from U.S. Africa Command.
The Pentagon on Monday identified the U.S. service member killed as Army Spc. Henry Mayfield Jr., 23, of Evergreen Park, Illinois. He was an air traffic services mechanic.
According to the news release on Sunday, the attack on the compound involved indirect and small-arms fire. There was an initial penetration of the perimeter, but Kenya Defense Forces and U.S. Africa Command repelled the al-Shabaab attack.
Kenya Defense Forces said the attempt was made at approximately 5:30 a.m. local time to breach security at Manda Air Strip and that it had successfully been stopped and the air strip was safe.
In addition to the casualties, six contractor-operated civilian aircraft were reportedly damaged to some degree, the U.S. Africa Command news release said.
The Kenyan military base has housed U.S. military personnel for years. It is unclear how many American personnel are stationed at the base that has reportedly been a site for U.S. special operations forces operating in Somalia.
"We remain committed to preventing al-Shabaab from maintaining a safe haven to plan deadly attacks against the U.S. homeland, East African and international partners," Townsend said in the Sunday afternoon news release.
Earlier, al-Shabab had said in a statement that some of its fighters had launched "a daring dawn raid on a U.S. naval base known as 'Camp Simba' in Lamu County, Kenya."
The al-Qaeda affiliate claimed that their fighters had taken control of a portion of the base, a claim that could not be verified.
Last week, al-Shabab carried out a car bomb attack in the heart of Mogadishu that killed at least 80 civilians.
"Al-Shabab is a brutal terrorist organization," U.S Army Maj. Gen. William Gayler in a statement. "It is an Al-Qaeda affiliate seeking to establish a self-governed Islamic territory in East Africa, to remove Western influence and ideals from the region, and to further its jihadist agenda. U.S. presence in Africa is critically important to counter-terrorism efforts."
About 500 U.S. troops are stationed inside Somalia assisting and advising that country's military in its fight against the terror group.
ABC News' Michelle Stoddart contributed to this report.