Clashes and another roadside bomb left nine people dead elsewhere.
In the eastern blast, one other U.S.-led coalition soldier was wounded when the roadside bomb hit their vehicle Monday in Kot district of Nangarhar province, the coalition said in a statement. The second soldier died of injuries shortly after the blast.
The troops were responding to a call from the local police who had discovered another explosive device nearby, when the second bomb exploded, the statement said.
The nationalities of the dead and the wounded soldiers were not released. The majority of the troops in that area are American.
A suicide attacker in the south, meanwhile, attacked a border police patrol Monday, leaving a policeman dead and four other officers wounded in Spin Boldak district of Kandahar province, said Gen. Abdul Raziq, the border security police commander.
In neighboring Helmand province, police discovered and tried to defuse a remote-controlled bomb in Nad Ali district, but it exploded, killing two policemen and two civilians, said provincial police chief Mohammad Hussain Andiwal. Four other civilians were wounded.
In the Zhari district of Kandahar, three Taliban militants were killed in a battle between police and NATO troops on Sunday, the Interior Ministry said. Another militant was detained in the operation, it said.
In neighboring Uruzgan province, a clash between NATO troops and Taliban insurgents near Tirin Kot, the provincial capital, left two civilians dead and five others wounded on Friday, the alliance said in a statement.
The violence followed a roadside bomb attack on NATO's International Security Assistance Force soldiers, the statement said.
One child was among the dead, while three were among the wounded, the statement said.
No soldiers were hurt, the statement said.
Civilians are often caught in the line of fire during fighting between the Taliban and international forces or during airstrikes by foreign troops because insurgents hide among civilian homes.
President Hamid Karzai last year pleaded repeatedly with NATO and the coalition to coordinate more closely with their Afghan counterparts to prevent civilian casualties.
Last year, insurgency-related violence left more than 6,500 people dead - a record number - including nearly 900 civilians, according to an Associated Press tally of figures from Western and Afghan officials.