Fighters from both sides say there have been heavy clashes near the Bagram air base, 50km (30 miles) north of the capital, Kabul.
Taleban sources claimed to have captured territory near the base from the veteran opposition commander, Ahmed Shah Masood.
But opposition officials said any lost ground had been retaken.
"It was a good offensive. We have broken their frontlines and our forces have gone further forward," a Taleban guard told the French news agency AFP.
He added that the fighting had been heavy at first, and appeared to have subsided later.
Opposition forces said early gains by the Taleban had been reversed.
"Initially they made some advances," said opposition aide Mohammed Yunus Qanooni.
"In our counter-offensive we took all the lost territory and they fled."
He claimed the counter-offensive had left 150 Taleban fighters dead.
Eyewitnesses
There are no independent sources to confirm the claims being made by either side.
However, eyewitnesses in the capital, Kabul, saw injured Taleban fighters being brought to the city's hospital.
Earlier, Taleban fighter jets flew low over Kabul and tanks were moved from locations in the city towards the front line.
The summer months in Afghanistan often witness an increase in the level of military activity.
The BBC's Owen Bennett-Jones says fears of a new offensive, which had been expressed during peace efforts, appear to have been well-founded.
Only last week, United Nations Secretary-General Kofi Annan called the situation "deplorable" and warned of a major round of fighting.
Militants
There has also been a renewal of the row over the alleged use of foreign fighters by the Taleban, who now control over 80% of the country.
The opposition say the Taleban have amassed Pakistani Islamic religious students and Arab militants on the frontline at the Bagram air base.
The Taleban say the only fighters they are deploying are Afghans.
"We have been fighting for 20 years and we don't need any help from anyone," said a spokesman.