An Afghan official also said fighting between supporters of rival warlords in northwestern Afghanistan killed four people.
The 70-year-old woman and her 30-year-old son were killed Monday in the village of Daigh, about five miles north of Musa Qala in the southern province of Helmand, said Amir Mohammad Akhunzada, the province's deputy governor.
Akhunzada did not identify the two but said the woman's son-in-law worked for the police. After the slaying, the militants threatened to kill anyone working for the government, he said.
"This hanging is totally against Islam," Akhunzada said. "They use the name of Islam to go against Islam."
The U.S. military said about 30 insurgents fired rockets and guns at a U.S. base late Tuesday in mountainous Nuristan province near the Pakistan border.
The statement said 15 insurgents were killed and two U.S. soldiers and one Afghan policeman suffered minor injuries. The base, which serves at the center of reconstruction projects for the region, was not damaged, it said.
Taliban fighters have stepped up attacks in southern Afghanistan this year. More than 900 people have died in violence since May, most of them militants killed in fighting with security forces.
The violence, the deadliest since the Taliban regime's ouster in late 2001, has underscored the weak grip of the government of U.S.-backed President Hamid Karzai, particularly in the volatile south and east of the country.
In the northwest of Afghanistan, some 400 militants were involved in clashes Monday in the Pashtun Kot district of Faryab province between forces loyal to rival ethnic Uzbek warlords Abdul Rashid Dostum and Abdul Malik, said Gen. Taj Mohammad, the Afghan National Army corps commander in northern Afghanistan.
Dostum is the current chief of staff of the Afghan Army's High Command.
At least one civilian was among the four people killed, and hundreds of others fled the fighting, Mohammad said.
The army and police sent hundreds of troops to restore calm and detained Khalem Salem, a Malik supporter who was involved in the fighting, Mohammad said.
It was not immediately clear what sparked the clashes, but the two groups had clashed 10 days earlier over a political dispute, leaving four dead.
Afghan police said a land mine killed a civilian woman driving on a highway in southern Afghanistan on Wednesday. A second woman and a child in the car were wounded, said Zabul province police chief Noor Mohammad Paktin, who blamed Taliban militants.
In Musa Qala, British troops in a NATO-led security force accidentally shot and killed an armed Afghan policeman wearing civilian clothes after mistaking him for an insurgent outside a base Tuesday, the British Ministry of Defense said.
Australia's government said Wednesday it will add 150 soldiers to the previously announced deployment of 240 next month to support Dutch troops in volatile southern province of Uruzgan. Australia already has 300 soldiers in Afghanistan, including 190 special forces soldiers.
In Canberra, Australian Prime Minister John Howard described Afghanistan's security as being at its worst since the fall of the Taliban.
"The level of violence has increased in Afghanistan in recent months as the Taliban and other terrorist groups including al Qaeda seek to chip away at the credibility of the Afghanistan government and prevent reconstruction taking place," Howard told Parliament.