At least 60 Taleban fighters have been killed in clashes with Afghan and US-led forces in southern Afghanistan, officials say.
In the first incident, in the province of Helmand, coalition forces responded to a Taleban attack, claiming to have killed 50 insurgents.
In the second, in neighbouring Kandahar province, 10 militants were killed in clashes with Afghan troops, police say.
The Taleban have rejected these reports of heavy losses.
Coalition forces say that the battle in Helmand lasted for more than 12 hours, and followed an attack by the Taleban against an Afghan army patrol.
"During the course of the battle, the insurgents attacked from 16 separate compounds using heavy machine-guns, rocket propelled grenades and small-arms weapons," a statement from the Combined Joint Task Force said.
"The Afghan national security forces and coalition forces immediately returned fire and called in close air support to destroy the enemy fighters within the compounds."
The statement claims no civilians were killed during the battle, but local people told a BBC reporter that most of the dead were women and children.
Reports of heavy Taleban losses were denied by one of their spokesmen, Qari Yusuf Ahmadi, who said that only one Taleban fighter was killed and three others injured.
The clashes happened near the town of Musa Qala, which has been the scene of some of the most hard fought and deadly battles in recent months.
Musa Qala has been a Taleban stronghold since October 2006, when UK troops withdrew from the town in a deal brokered by local tribal elders with the militants. British forces say the Taleban broke the deal and overran the town.
In the second of Thursday's incidents, insurgents ambushed a patrol of the Afghan National Army in the province of Kandahar, a statement by the Combined Joint Task Force says.
According to the police, 10 Taleban fighters and a policeman were killed.
Violence has risen sharply in the last two months, as Taleban attacks on Afghan and US-led forces have increased, as part of their summer offensive.
Many of those killed have been militants, but the death toll among civilian and coalition forces has also risen.