The clash in the mountains of southern Helmand province also left three wounded, said the deputy governor Amir Mohammed Akhunzanda. Police arrested three suspected Taliban and recovered weapons, he said.
Insurgents also killed four police in southeastern Afghanistan on Monday as they went to help a local official who had been ambushed by militants, authorities said.
The clash happened in Giro district of Ghazni province as the officers rushed to repel an ambush on the district government's chief, said Abdul Ali Fakuri, spokesman for the provincial governor.
Insurgents killed four police. Other Afghan and U.S.-led coalition forces rescued the chief unharmed
Over the past year, a growing insurgency has gripped the country's south and east, but Kabul, patrolled by thousands of NATO-led foreign troops, has been largely spared. However, a series of recent bombings have rattled the capital, the latest on Monday.
The first bike bomb blast struck Kabul's northern neighborhood of Khayrkhana as a NATO patrol passed by, smashing the windows of a nearby car, police official Ali Shah Paktiawaal said. Four soldiers were slightly hurt, NATO said, adding a second bomb at the scene was discovered and disarmed, NATO said.
Another bomb-rigged bicycle blew up as a NATO vehicle was passing on a main road near a U.N. office, an Interior Ministry spokesman said.
The bomb exploded prematurely and did not cause any damage or casualties, he said, adding a suspect had been arrested.
NATO confirmed the attempted attack.
In southeastern Paktika province, a suicide car bomber targeted Afghan troops shopping in a bazaar on Monday, wounding six soldiers and one civilian, an official said.
The bomber, driving a taxi, drove to within 40 yards of the soldiers in Barmal district before his vehicle exploded, said Sayed Jamal, the governor's spokesman.
A would-be suicide bomber on a bicycle attacked a police pickup truck in central Logar province Monday, wounding himself but causing no other casualties, said Gen. Mohammed Mustafa, the province's police chief. The police vehicle was damaged and the militant was arrested, he said.