Two gun battles with Afghan troops and police in the Ghazni province, south of Kabul killed 16 Taliban fighters, according to local government spokesman Abdul Ali Fakuri. An Afghan soldier was also killed and two policemen were wounded, he said.
Three Taliban fighters were killed late Monday in a village in southern Kandahar province, the Taliban's birthplace, provincial governor Asadullah Khalid said.
"The Taliban entered Afghanistan from Pakistan. Fighting erupted and three Taliban were killed," he said.
Operation Medusa
NATO says a major offensive codenamed Operation Medusa in Kandahar's Panjwayi and Zhari districts has killed over 500 rebels since September the 2nd but the Taliban rejects that figure.
Seven suspected rebels have been detained as NATO troops try disrupt insurgent supply lines between Kandahar and neighbouring Helmand province, the alliance said in a statement.
Meanwhile four militants died Monday in a gunbattle with Afghan troops in eastern Paktia province's Zurmat district, the interior ministry said. Three other fighters were captured.
Paktia's governor Hakim Taniwal, whose family lives in Australia, was killed in a suicide bombing on Sunday. Six people attending his funeral died in another suicide blast.
Another Taliban insurgent was killed Monday by Afghan and NATO troops in northern Balkh province, a police official said. Two insurgents were also killed the same day in Paktika province, the ministry said.
Meanwhile 10 suspected insurgents were captured in Logar province, south of Kabul, the ministry said. "A large number of weapons, explosives and other bomb-making devices were also seized with the men."
Warlord detained
Separately, Afghan and US-led coalition forces detained a commander of warlord Gulbuddin Hekmatyar's Hezb-e-Islami militant group, who was also a "known al-Qaeda facilitator," a coalition statement said. Six of his associates were also detained in the arrests in eastern Nangarhar province.
Another man was seized while laying a mine on a road used by Afghan and foreign troops in Ghazni province, Afghan officials said.
Elsewhere a US soldier was killed and another injured when their armoured vehicle overturned in Asadabad, the capital of eastern Kunar province, the coalition said.
The latest violence comes as the top British general in charge of NATO forces in Afghanistan said that his men were defeating the Taliban regime which continues to wage a bitter insurgency.
Lieutenant General David Richards told Britain's Daily Telegraph that his forces were winning. "I believe that we are in the process of establishing psychological ascendancy," he said.
Drugs
Meanwhile, the head of the United Nations office on drugs and crime, Antonio Maria Costa, has called for strong military action by NATO forces to destroy the opium industry in southern Afghanistan.
A UN report says the impact of a “staggering” 59 percent annual increase in opium cultivation has led to a bumper crop of 6,100 tons of opium in 2006. Afghanistan is estimated to supply 92 percent of the world’s opium.
"In the turbulent southern region, counter-insurgency and counter-narcotics efforts must reinforce each other so as to stop the vicious circle of drugs funding terrorists and terrorists protecting drug traffickers."
"I call on NATO forces to destroy the heroin labs, disband the open opium bazaars, attack the opium convoys and bring to justice the big traders. I invite coalition countries to give NATO the mandate and resources required," Mr Costa said.
But NATO Secretary General Jaap de Hoop Scheffer rejected the demand. "NATO does not have and is not seeking a leading role in the indeed very important fight against narcotic trafficking," he told reporters. "I think its a wrong approach."
The alliance has attempted to confine its role to military action and reconstruction.