In the north a Taliban-era mass grave was discovered, a police spokesman said.
The clashes with militants occurred in two different mountainous areas of Zabul province late Friday, said provincial deputy governor Ghulab Shah Alikheil.
The operation was aimed at militants responsible for Tuesday's ambush of a road construction crew in the province. That attack killed 17 people and 16 others wounded, Alikheil said.
The clashes in the south killed 24 militants and wounded eight. There were no casualties among the Afghan or foreign joint forces, however, he said.
Saturday's suicide attack killed two members an Indian road construction crew in the southwestern province of Nimroz and wounded eight other people including five Indian workers, said Gov. Ghulam Dastagir.
The bomber approached the site on foot, he said.
"(The Taliban) are conducting these suicide attacks and terrorist attacks to stop the development and reconstruction in Afghanistan," Dastagir said.
Road-building is a key part of Afghan reconstruction and many projects are in remote, insurgency-plagued areas. Militants have targeted work crews in roadside bomb attacks, ambushes and kidnappings, killing or wounding dozens of workers and their private security guards.
The Indian Foreign Ministry identified the two dead engineers as M.P. Singh and C. Govindaswamy, both from its Border Roads Organization.
Suicide attacks in Afghanistan spiked in 2007, with the Taliban launching more than 140 such missions - the highest number since the radical Islamist group was ousted from power by a United States-led invasion in 2001.
The United Nations says more than 8,000 people were killed in insurgency-related violence in 2007.
Meanwhile, a Taliban-era grave containing more than 100 bodies of soldiers and civilians was found after it was exposed by weather and erosion in the northern province of Balkh. Area residents had buried the dead after Taliban militants stormed the city in the late 1990s and killed dozens of people, said Sher Jan Durani, spokesman for the provincial police chief.