The U.S. military has not released any other details on the attack, saying it is awaiting next of kin notification.
But a webpost by Col. Arthur Sellers, the commander of the 3rd Brigade, 82nd Airborne Division, confirmed that two paratroopers from his unit had been killed in Afghanistan on Monday.
"It is with a heavy heart that I inform you of the loss of two Paratroopers from the Brigade during combat operations," he wrote. "I ask you to respect the official Department of Defense notification process, a process which may take a few days. If you receive any information about these combat operations, either factual or speculative, I ask you to refrain from sharing it for the sake of the Paratroopers’ loved ones."
An Afghan security source told ABC News that an Afghan army soldier opened fire inside Tanajoh military camp in the Shahwali Koot district of Kandahar province in the south. The attacker was killed in return fire, the source said.
In a statement, the Taliban said an "unidentified Afghan soldier fired his gun ... killing two U.S. soldiers and wounding three."
The violence followed a deadly day on Sunday, when a suicide bomber attacked the offices of President Ashraf Ghani's running mate and former chief of intelligence. At least 20 people were killed and about 50 were wounded.
The U.S. is about to start its eighth round of negotiations with the militant group in Qatar shortly, as the Trump administration moves to draw down the American military presence in Afghanistan nearly 18 years after the U.S. first invaded.
Pompeo said Trump had directed him to reduce U.S. troops before the 2020 presidential election.
"He's been unambiguous: end the endless wars. Draw down. Reduce," Pompeo said Monday in Washington, adding with a smile, "It's not only my expectation. It would be job enhancing."
Chief U.S. negotiator Zalmay Khalilzad said earlier this month those talks had made substantial progress, in particular on a timetable for U.S. withdrawal and getting a Taliban commitment to preventing Afghanistan from becoming a terror safe haven.
But critics, including some senior Afghan government officials, say the peace process has been dangerously flawed by keeping the Afghan government out of the talks so far. Other critics have questioned how the Taliban can commit to rooting out terrorism or why the U.S. would trust the group's commitment, with details of any agreement so far still tightly held.
Khalilzad said on Sunday that talks between Taliban and Afghan government representatives would take place once the U.S. and Taliban reached an agreement. But the Taliban, which refuses to meet with the government because it calls it a U.S. puppet, will be meeting not one-on-one with government leaders, but a "national negotiating team," Khalilzad said.