"At least 34 enemy dead bodies are at the battlefield, but we believe there are many more killed."
More Taliban fighters were reportedly killed in an operation against suspected Taliban fighters in a district they captured three days ago, a defence ministry spokesman said.
Afghan soldiers backed by Nato ground and air support launched an offensive in the remote Ajristan district of central Afghanistan's Ghazni province, killing at least 15 fighters, during an operation to retake control of the area, an Afghan official said on Thursday.
Ismail Jahangir, a government spokesman, said: "At least 15 Taliban have been killed and several others are wounded since [Wednesday]."
The operation continued for a second day on Thursday, with the troops able to recapture the district headquarters compound but still fighting for wider control, Jahangir, a government spokesman said.
The Nato-led International Security Assistance Force (Isaf) said: "The joint operations began with a co-ordinated air strike on Taliban fighters, inside Ajiristan. Several insurgents have been killed and wounded.
Ajiristan was previously captured by the Taliban in October 2007, and was retaken the following day when at least 300 security forces moved into the district centre.
The Taliban have captured several mainly remote districts in the past but have not been able to retain hold of them for long, although there are a handful in the southern Helmand province, that security forces admit are in rebel control.
The fighting in Afghanistan meanwhile continued to take its toll on international forces. In the latest loss, a British soldier was killed in southern Afghanistan, the UK defence ministry said on Wednesday.
A ministry spokesman said no further details were immediately available.
Meanwhile Hamid Karzai, Afghanistan's president met Jaap de Hoop Scheffer, the Nato secretary general, to discuss the security situation in the country.
Karzai told to James Bays, Al Jazeera's correspondent in Kabul, that things were not as good as they should be, but not as bad as reports had suggested.
"We are continuing in a struggle against terrorism. The cross-border activity that's affecting us very seriously is a concern for us. The provinces of Afghanistan closer to Pakistan are under threat, and some of them under serious threat, no doubt," he said.
"The country is, as far as progress and economic reconstruction is concerned, heading in the right direction," he said.
Nato's Scheffer said that Nato would not enter Pakistan to hunt the Taliban, but reserved the right to attack them there should they launch cross-border attacks.
"We have a United Nations security mandate for Afghanistan and that's it. If Nato forces are shot at from the other side of the border, there is always the right to self-defence but you will not see Nato forces crossing into Pakistan territory," he said.