The three policemen were unarmed and walking home after work in Charchino district when suspected Taliban opened fire on them, provincial governor Jan Mohammad told AFP on Wednesday.
A US soldier and an Afghan interpreter were killed in the same province on Tuesday when a bomb hit their vehicle, the US military said.
“They were part of a convoy to re-supply forces conducting operations aimed at defeating enemy forces in the area at the time of the detonation,” it said in a statement.
Police and soldiers are among the main targets of a rebellion blamed on the Taliban, deposed in a US-led campaign in late 2001.
Meanwhile, the Taliban claimed responsibility for killing an Indian engineer who was abducted on Saturday and found dumped on a roadside in the southwestern province of Nimroz on Wednesday.
“Police have found the body of the Indian national and I can confirm that he has been killed,” Nimroz district chief Mohammad Hashim told Reuters.
The young man had been beheaded, according to Amanullah Khan, chief of highway police in the province.
The head had been placed with the body and a note found, apparently written in English, Khan said.
“Police have found the body of the Indian national and I can confirm that he has been killed”
Afghan President Hamid Karzai condemned the killing and vowed to provide security to foreigners involved in reconstruction works in the war-ravaged country.
Indian Prime Minister Manmohan Singh also condemned the Taliban and referred to the slain engineer, Maniyappan Raman Kutty, as a “soldier of peace”.
A Taliban spokesman, Qari Mohammad Yousuf, said on Tuesday Kutty had been killed after a deadline passed for his company to announce its withdrawal from Afghanistan.
India has good relations with Afghanistan and hundreds of Indians are working on Afghan reconstruction projects.
In the past, the Taliban have kidnapped several Indian and Turkish engineers involved in rebuilding roads.
Two Indians seized by suspected Taliban members while working on a US-funded road project in late 2003 were released unharmed after nearly three weeks in captivity.
A Turkish national was killed but several others were freed, apparently after ransoms were paid.
Kutty’s killing comes amid a spate of rebel violence.
This year has been the deadliest for violence involving anti-government fighters, with nearly 1500 people killed – most of them suspected rebels involved in clashes with Afghan and US-led forces.