Thirty Taleban fighters and two members of the security forces have died in an intense military clash in north-west Afghanistan, the authorities say.
Militants attacked police posts in Badghis province, near the border with Turkmenistan. The Taleban have disputed the government's account.
There were also reports that 27 fighters have been killed in the southern Zabul province.
Separately, a general has been shot dead in the southern city of Kandahar.
The city's chief police officer said Gen Daoud Salehi, who was training a local police force, was shot dead while having his hair cut in the city centre.
'Back under control'
The police chief of Badghis province told the BBC that a large number of Taleban insurgents had launched an attack in a remote district on Saturday afternoon.
He said that in six hours of fighting, 30 of the Taleban and two policemen were killed, adding that the district was fully back in government control.
A Taleban spokesman, also talking to the BBC, contradicted this account, saying the rebels were in control of the district and inflicted heavier casualties on the government side.
This part of Badghis did see a big battle four years ago, but more recently it has not seen the scale and frequency of violence regularly occurring in the south and east.
In the south, Nato and Afghan troops clashed with militants and called in air strikes, leaving 27 suspected Taliban insurgents dead in the district of Shinkay, the Associated Press news agency quoted a Defense Ministry spokesman as saying.
The operation followed intelligence reports of militant activity in the area, the spokesman said. There were no reports of civilian casualties.
In additional incidents over the past couple of days, a British soldier has died in Helmand, also in the south.
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Afghanistan map