The Canadian soldier was killed and several others wounded in dawn gunfire from US jets in a friendly fire incident during Operation Medusa.
Troops battling Taliban insurgents in the Panjwayi district of southern Kandahar province had called for air support, NATO's International Security Assistance Force said in a statement.
"Two ISAF jets, confirmed by the Combined Air Operations Centre as US A-10s, provided the support but regrettably engaged friendly forces during a strafing run, using cannons," it said.
The incident resulted in "one Canadian death and multiple casualties".
ISAF commander Lieutenant General David Richards told reporters the incident was "regrettable".
"But the task they were set is extremely important, perhaps vital to the operation we are conducting here," the British general said.
Probe to be launched
NATO's military commander announced a probe into the friendly-fire incident.
"The commander of regional command (south) has ordered an investigation into this incident and will make recommendations to limit the possibilities of a similar tragedy from happening again," US General James Jones said.
"While friendly fire incidents are horrible and we do everything to reduce the chances of them occurring, accidents do happen," General Jones said in a statement from NATO headquarters in Mons, southern Belgium.
He also conveyed his sympathies to the victims and their families, and expressed his determination that the alliance's mission to bring security to all of Afghanistan would succeed.
Four Canadian soldiers were killed by friendly fire in April 2002 when a US F-16 fighter pilot mistook troops in a live-fire training exercise for Taliban fighters and dropped a 500-pound laser-guided bomb on them.
The pilot was found guilty of dereliction of duty, reprimanded for "willful misconduct" and fined.
Four other Canadian soldiers involved in the operation were killed on Sunday. Twenty Canadian soldiers have now been killed in hostile action in Afghanistan this year. There are about 2,300 in Afghanistan.
The operation was launched Saturday and involves about 2,000 ISAF and Afghan soldiers and support staff and is aimed at driving seasoned Taliban fighters out of Panjwayi.
This was the first such incident in more than 800 ISAF operations involving close air support, he said.
British casualties
Sixteen Taliban and three police were also killed in a battle overnight when rebels tried to retake a southern town they had captured briefly weeks ago.
A suicide blast struck a British patrol on a road in the east of the city that is regularly used by foreign troops and has seen most of the suicide blasts in the city.
Britain's Ministry of Defence said in London that one British soldier was killed and another was badly injured in the bomb attack.
NATO's International Security Assistance Force (ISAF) said two others were lightly hurt.
The head of the police criminal investigation department, General Alishah Paktiawal, told AFP that the dead Afghans included three passers-by and a member of the Afghan intelligence agency.
It brings the country’s death toll in Afghanistan this year due to hostile action to 14 troops.
That number excludes 14 others who were killed in the southern province of Kandahar on Saturday when a reconnaissance plane supporting Operation Medusa crashed because of a technical problem.
It was the single biggest loss of British troops in Afghanistan or Iraq since the US-led "war on terror" was launched in November 2001.
“Stand-firm”: Blair
In Iraq two British troops were killed and a third seriously injured when insurgents attacked an army unit escorting a reconstruction team near Basra in the south of the country.
British Prime Minister Tony Blair said that his nation must “stand firm” against a global terrorist threat on the back of the news of the British deaths in Iraq and Afghanistan.
Mr Blair has described the deaths of the three soldiers as a “terrible tragedy in particular for the families of the servicemen involved.”
Meanwhile, a British national was killed and two others were wounded by a gunman at a Roman amphitheater in downtown Amman.
The prime minister said that it was important that Britain stopped Afghanistan from becoming a training ground for terrorists.
"It's so important for us to make sure we stand firm in Afghanistan and stop that country being a training ground for the export of terrorism around the world."
"We should be very grateful and very proud of the fact that Britain's armed forces are prepared to stand up to this threat."
Referring to the attack in Amman, Mr Blair said: "The global terrorist threat, which is trying to stop these countries getting on their feet or to kill vulnerable, innocent people, like has happened today in Jordan, is aimed to make us lose heart and make us fearful about standing up for what is right.
"Our response has to be to stand firm."