If the estimate is confirmed, the battle would be one of the deadliest since U.S.-led forces ousted the Taliban regime five years ago.
The operation took place near Kandahar, where anti-Western forces seem to be gaining strength, reports CBS News correspondent Dan Raviv. One way to measure the strength of the Taliban is by how much opium is grown.
Up almost 50 percent from last year, more opium than ever is being grown in southern Afghanistan — the area where the Taliban fighters are strongest. And almost five years after the government was pushed out of Kabul, opium poppies are spreading like weeds, financing the Taliban's comeback.
"The Taliban is starting to tell people on the ground that they must grow poppies and the reason is because they want the money. So, they're getting money from the poppy growth," says CBS News consultant Jere Van Dyke.
Reporters could not reach the combat zone because officials barred traffic from all but one road in this part of southern Kandahar province.
An Associated Press reporter who traveled to Pashmul saw warplanes drop five bombs within about 20 minutes on orchards where militants were believed to be hiding.
Explosions echoed across grape and pomegranate fields and clouds of dust rose amid the greenery and dried-mud houses of the Panjwayi district, which is about 12 miles from Kandahar city.
Operation Medusa was launched Saturday to flush out Taliban fighters from Panjwayi and neighboring Zhari district. NATO spokesman Maj. Scott Lundy said alliance and Afghan troops had gained ground and disrupted the militants' command system so guerrillas were moving in confusion.
Afghan Defense Minister Abdul Rahim Wardak said Taliban casualties were high, but could not confirm the NATO report of more than 200 dead.
A NATO statement said its figure was derived from "surveillance and reconnaissance assets operating in Panjwayi and Zhari districts, as well as information reported by various Afghan officials and citizens living nearby."
About 80 other suspected Taliban were arrested by Afghan police and a further 180 fled the area, it said.
The alliance said it had no reports of civilian casualties, despite the heavy weight of fire being used. But a spokesman for the Afghan Defense Ministry, Gen. Zahir Azimi, said earlier that an undetermined number of civilians were killed.
Jason Husiak, a spokesman at the Canadian Department of National Defense, said four Canadian soldiers died in Sunday's fighting and others were wounded.
NATO said seven soldiers in its International Security Assistance Force were wounded, one seriously. The other six were expected to return to duty within a few days, it said.
There was no word on any casualties among Afghan troops.
On Saturday, a reconnaissance plane supporting Operation Medusa crashed, killing allon board. NATO said the crash was not caused by hostile fire, saying the plane reported a technical problem before it went down. Investigators examined the wreckage Sunday.
The weekend's fatalities increased the total of foreign troops killed in Afghanistan so far this year beyond the 130 who died during all of 2005 — an indication of the escalation in violence sparked by an upsurge in Taliban attacks.
NATO forces took command of security in Kandahar and other provinces in Afghanistan's volatile south from a U.S.-led coalition Aug. 1 amid the worst fighting since the Taliban fell in late 2001.
According to an AP tally of figures from NATO, the U.S. military and Afghan officials, more than 1,800 people, most of them militants, have died in violence the past four months.
Insecure conditions have made it increasingly difficult for civilians, aid workers and journalists to travel outside the main cities in the south.
After Operation Medusa started, authorities in Kandahar warned people not to travel off the main highway in the province, which leads into Panjwayi. The road was blocked by soldiers Sunday — not far from where bombing was taking place. Some military Humvees were parked nearby.
Ikram Ullah, an Afghan soldier at the roadblock, said he had heard that 60 or 70 Taliban had been killed by warplanes and helicopter gunships since Saturday morning.
He said most of the families in the area fled after they were told to evacuate — although some civilians were nearby. A few children watched the bombing from the road.
"Only the Taliban are in the village," Ullah said, pointing toward the orchards, where clusters of homes were scattered among trees and vines.