An Afghan commander said on Saturday that the troops were travelling close to the Pakistan border. A spokesman for the Taliban claimed responsibility for the blast, one of the bloodiest in months.
The 10 soldiers from a border guard unit were aboard a pickup when it struck the landmine on a road near Spinboldak, a frontier town in southern Kandahar province, General Abd al-Raziq Khan, the unit's commander, said.
The only survivor, an officer called Qadir Bhai, was seriously injured and taken to a nearby French special forces base for treatment, Khan said.
He said the mine was freshly laid and blamed Taliban fighters for the attack.
"They are coming over the border from Pakistan to carry out these attacks," he said in a telephone interview from Spinboldak.
Mullah Abd al-Hakim Latifi, a man who regularly claims to speak for the Taliban, said its members detonated the mine by remote control and then opened fire on the stricken soldiers.
He said 11 troops were killed and vowed the conservative group would continue to attack Afghan and American forces.
Another mine on Thursday reportedly wounded four Afghans working for a US security firm in eastern Afghanistan.
More mine explosions
The four were wounded when a mine exploded near their vehicle in the Chawkay district of Kunar province, Interior Ministry spokesman Latfullah Mashal said.
Mashal said the men were working for a US contractor called USPI, which provides security for a Turkish construction company repairing the province's main road. A Turkish man working on the road was abducted and killed last month.
A Turkish engineer was killed in
the Kunar province last month
Two of the injured were taken to hospital in Jalalabad while two others were treated at the scene, Mashal said.
He said investigators were unsure if the mine was newly laid or a leftover from Afghanistan's many years of war.
US and Afghan security forces are in the midst of a winter-long operation supposed to keep militants on the defensive and prevent them from preparing major violence against Afghan parliamentary elections due to be held in the spring.
Commanders have said the operation includes fresh efforts to tighten security along the mountainous border with Pakistan, where fighters are believed to find refuge between attacks on American and Afghan troops.
In another incident, an Afghan border guard died on Saturday in the southeastern Khost province after a gunman tried to extort money from a car full of guards at an illegal checkpoint, police said.
The gunman, who opened fire on the car when the soldiers refused to pay, was also fatally shot, police chief Muhammad Ayoub said.