The deadly shooting as the latest case of so-called "insider attacks," instances when an Afghan policeman or soldier — or a Taliban insurgent wearing a police or military uniform — turns his weapon on Afghan forces or international troops.
Last week, two American soldiers were shot and killed by an Afghan soldier in the same Kandahar district. The attacker, who was wounded and taken into custody, was dubbed a "hero" by the Taliban, though the insurgents did not claim the assault.
The latest attack in Kandahar took place on Sunday, and the attacker fled the scene, said Jamal Naser Barekzai, a provincial spokesman. He added that an investigation is underway.
Taliban spokesman Qari Yusouf Ahmadi claimed the attack and said the policeman had joined their ranks.
In last week's attack, the U.S. Defense Department said 20-year-old Pfc. Brandon Jay Kreischer of Stryker, Ohio, and 24-year-old Spc. Michael Isaiah Nance of Chicago died "as a result of wounds sustained in a combat related incident" in southern Afghanistan.
Both soldiers were assigned to the Army's 82nd Airborne Division, based in Fort Bragg, North Carolina.
The Taliban also claimed an attack on a checkpoint that killed 11 security forces Sunday in northern Jawzjan province, said Faridon Aneeq, spokesman for the provincial governor.
Elsewhere, a female police officer was shot dead Monday while traveling through the northern Balkh province, said Adil Shah Adil, provincial police chief's spokesman. The Taliban did not comment on the incident.
The Taliban now effectively control half the country and stage near-daily attacks, mainly targeting Afghan security forces and government officials or those they see as siding with the government. Many civilians caught in the crossfire are also killed.
Since late last year, the insurgents have been meeting with U.S. envoy Zalmay Khalilzad for talks on finding a peaceful resolution to the nearly 18-year war, America's longest conflict.
After visiting Kabul and Islamabad for another round of talks, Khalilzad travelled last week to the Gulf Arab state of Qatar, where the Taliban maintain a political office, to talk to the insurgents. The Taliban refuse to negotiate directly with the government in Kabul, considering it a U.S. puppet.
Suhail Shaheen, a Taliban spokesman at the Doha office, tweeted on Sunday that the Taliban and Khalilzad "started talks today and the process may continue for few days."
"If the agreement is finalized, then all foreign troops will quit Afghanistan in a specified timeframe that will pave the way for dialogue with all Afghan sides," he added.
In another development Monday in Afghanistan, the Islamic State group claimed responsibility for an explosion involving a bus carrying media workers in the capital, Kabul, the previous day.
A magnetic explosive device attached to the bus killed two on Sunday, the bus driver and a pedestrian, according to Nasrat Rahimi, the Interior Ministry's spokesman. Two employees of the Khurshid TV station and another pedestrian were wounded in the attack, he said.
Afghan President Ashraf Ghani condemned the attack. "Deliberately targeting the media and civilians is a war crime and those responsible will be held accountable," he tweeted.