The bomber, carrying explosives strapped to his body, attacked a police patrol in Nad Ali district in Helmand province, said Ghulam Nabi Mulakheil, the provincial police chief.
Two officers and the bomber were killed in the blast, Mulakheil said.
Helmand province is the world's largest opium-producing area. Last month, NATO launched its biggest anti-Taliban offensive there.
In eastern Paktika province, militants attacked a police post in Gomal district, killing one officer and wounding two others, said Mohammad Akram Akhpelwak, the provincial governor.
Militants also destroyed an old government compound in the area, he said.
In southwestern Farah province, militants attacked a police checkpoint in Bala Buluk district, and in the ensuing clash three policemen went missing, said Abdul Mubin Rashid, a spokesman for provincial governor. It wasn't clear if the officers were kidnapped or killed in the gun fight.
A suicide car bomber, meanwhile, blew himself up as police chased him in a car, also in Farah province, the interior ministry said in a statement.
Also Saturday, U.S.-led coalition troops detained 10 men in neighboring Zabul province, suspected of helping foreign fighters in Afghanistan, the coalition said in a statement.
Troops raided several compounds in Zabul's Qalat district early Saturday, the statement said. There were no reports of injuries during the raid.
Last week's clashes in western Afghanistan, which local and U.N. officials said left dozens of civilians dead, also killed more than 10 Taliban commanders, the coalition statement said.
Initially, the U.S. military said international and Afghan troops killed 136 suspected Taliban fighters in the Zerkoh Valley of Herat province, in some of the deadliest fighting so far this year.
However, an investigation by Afghan officials found that 51 civilians died — including women and children — prompting President Hamid Karzai to warn that Afghans can no longer accept such civilian losses.
Gen. Dan McNeill, commander of NATO's International Security Assistance Force, said Friday he was personally examining detailed battlefield reports. He insisted only militants were targeted.
Adrian Edwards, spokesman for the United Nations mission in Afghanistan, said Friday a separate investigation by its officials found up to 49 civilians were killed and more than 900 families displaced because of fighting.
The Afghan and U.N. officials did not provide details of how they reached their conclusions.
In its statement, the coalition said one of the suspected Taliban commanders killed was a militant from southern Helmand province, released from an Afghan jail last month in exchange for a kidnapped Italian reporter.