At least 22 people are reported to have been killed in the latest violence in Afghanistan - 19 of them Taleban fighters and three policemen.
Six UK soldiers have been killed in recent weeks
The Taleban were killed in fighting with UK troops and Afghan police in the southern Helmand province, local officials say.
The police were killed by suspected Taleban fighters in Ghazni province.
On Saturday six civilians and two Canadian soldiers were killed in a double suicide attack in Kandahar.
"Government and British forces killed 19 Taleban and arrested 17 others, including two Pakistanis, in the attacks" in Helmand, the province's deputy governor, Amir Mohammad Akhundzada told the Reuters news agency.
Local people said civilians had also been killed.
The fighting took place when the UK and Afghan forces attacked Taleban positions in villages close to the provincial capital, Lashkar Gah, Mr Akhundzada said.
The three Afghan policemen were killed when their post was attacked in the town of Gelan in Ghazni, local officials said.
Laden with explosives
A spokesman for the US-led forces in Afghanistan, Major Scott Lundy, said Saturday's suicide attacks in Kandahar city would not deter the coalition from its task of promoting security and bringing development in Afghanistan.
The two Canadian soldiers died, and eight others were hurt, when a car laden with explosives rammed into their convoy.
Soon afterwards near the scene, a second bomber killed six Afghans.
Nineteen Afghan civilians were also injured. Both bombers died in the attacks.
A man who claimed to be a spokesman for the Taleban told reporters by telephone that the movement was behind the attack.
He threatened more suicide attacks and ambushes against the US-led coalition and Afghan forces.
On Friday the most senior British military commander in Afghanistan said the situation in the country was "close to anarchy", with feuding foreign agencies and unethical private security companies compounding problems caused by local corruption.
Lt Gen David Richards, the head of Nato's international security force in Afghanistan, warned in an interview with the Guardian newspaper that coalition troops lacked necessary equipment.
Al-Qaeda and Taleban militants have mounted a series of attacks in Afghanistan in recent months.
Most of the violence has been in the south and east, in provinces bordering Pakistan.
Nato is due to take over operations from the Americans in southern Afghanistan later this year, and is expected to deploy up to 21,000 soldiers there.