Four soldiers with the Nato-led International Security Assistance Force (ISAF) were killed and seven wounded during two days of fighting after Operation Medusa was launched in a Taliban stronghold in southern Kandahar province on Saturday.
Afghan officials said the four dead were Canadian troops.
The operation, involving about 2,000 Afghan and Nato personnel, is the biggest offensive since troops from ISAF took command of the south on July 31, and is aimed at driving out insurgents in Panjwayi district.
Afghan and ISAF troops gained ground and a "significant number of suspected insurgents were detained", the force said in a statement.
General Aziz Wardak, Kandahar province police chief, confirmed that a "number of suspected" Taliban had been arrested.
Military officials have long said that rebels are massing in Panjwayi, about 35km (20 miles) west of Kandahar, Afghanistan's second-largest city. There has been fierce fighting in Panjwayi this year.
The Taliban emerged from the area as an armed force in the early 1990s, first capturing Kandahar and then sweeping to power in 1996 before being ousted five years later for sheltering Al-Qaeda after the September 11 attacks.
The bodies of 14 British soldiers have been retrieved from the wreckage of their reconnaissance plane that came down
"We were doing a very detailed survey of the target and that aircraft was part of assets to do that survey and to ensure non-combatants were not injured in the operation"
Major Quentin Innis, ISAF spokesman in Kandahar
near Panjwayi on Saturday.
ISAF has dismissed a claim by the Taliban that they had shot the aircraft down, saying the crash was caused by a technical problem.
"It was flying far too high when the crew reported a problem," it said in a statement.
The crash caused the biggest single loss of British troops in Afghanistan or Iraq since the US-led "war on terror" was launched in November 2001. The plane had been despatched from a base in Qatar.
The remains of the British soldiers were due to be transported from the crash site to the Kandahar air field on Sunday before being repatriated to Britain.
British forces form the bulk of an ISAF deployment of about 10,000 troops in southern Afghanistan, with major contributions also coming from Canada and the Netherlands.
The troops have suffered a barrage of attacks, with more than 80 foreign soldiers killed in hostile action in Afghanistan in a surge in Taliban violence this year, particularly in the south.
Mark Laity, Nato's civilian representative, told reporters on Sunday that the rebels were allowed to re-group in the south, primarily because there were not enough troops in the area before ISAF was deployed.
Lieutenant General David Richards, ISAF commander, said in an interview published at the weekend that the force had set itself a six-month deadline to establish a clear advantage over Taliban insurgents.
Meanwhile, Des Browne, Britain's defence secretary, has defended the safety record of the Nimrod reconnaissance plane following the crash.
UK has defended the safety record
of the Nimrod reconnaissance plane
Browne told BBC television that the Royal Air Force, which operates 16 Nimrod MR2 aircraft out of RAF Kinloss in northeast Scotland, had an "excellent record of maintaining and supporting its aircraft to the highest standards".
But despite his assurances that the plane, which is based on the world's first jet airliner the De Havilland Comet, is a "very safe aircraft", checks are being carried out on the entire fleet.