The clashes come amid stepped up US-led military efforts to crush armed extremists, primarily the Taliban, behind an insurgency in Afghanistan.
Afghan army and coalition forces attacked around 40 rebels on Thursday and Friday in the southern Uruzgan province "in an effort to disrupt and deny enemy operations in those areas," a coalition statement said.
"Patrol reports and debriefings concluded that an estimated 31 enemy extremists were killed during engagements in Chora, Kala Kala, and Khorma villages," it said.
Another 10 were killed on Saturday in an early morning air assault on "several known extremist targets" in Sangin, in the southern Helmand province, one of the areas worst hit by a Taliban insurgency and where more than 2,300 British troops are based.
A major British operation is under way in Sangin, where a British base has come under regular attack in recent weeks and five British soldiers have died in hostile fire since late June.
Meanwhile, the defence ministry announced that the Afghan army had killed another eight rebels in Sangin on Friday.
Four others were killed on Friday in southern Zabul province in a gunfight that erupted after they attacked a military patrol, the ministry said in a statement.
In the same province on Saturday, an Afghan civilian was killed and a civilian driver wounded when rebels attacked a convoy of trucks supplying US forces, Zabul's police chief, Noor Mohammad Pakteen, said.
In the subsequent fighting, two Taliban were killed and one was captured, Pakteen said.
And in Uruzgan province, troops killed two foreign nationals who had been wearing burqas, the all-covering garment worn by women in Afghanistan, on Friday. The rebels had used burqas to hide their identity.
The US-led coalition said in a statement that the pair were "extremist suicide bombers disguised as women."
The violence in southern Afghanistan has been the most severe since the toppling of the Taliban from government by a US-led invasion in late 2001.
About 800 people, the majority of whom were Taliban rebels, have died since mid-May when Afghan and coalition forces launched Operation Mountain Thrust, their biggest anti-Taliban operation.
Separately, the US military said it would co-operate with an Afghan government team probing reports of civilian casualties in a southern air raid on Monday in Uruzgan's provincial capital of Tirin Kot.
The military, however, said in a statement that it has no information to support claims that civilians were killed or wounded in the raid that US forces estimated killed more than 40 Taliban members.
Local residents wounded in the assault have said at least four civilians, including children, were among those hurt.
On Thursday, Hamid Karzai, the Afghan president, ordered an inquiry into the reports. A five-member team of officials has traveled to the city to interview local authorities and residents.
Karzai has previously criticised heavy-handed coalition attacks that have killed civilians.