Two truck drivers were also killed in Laghman, eastern Afghanistan, in an ambush by Taliban fighters, the interior ministry said.
There are fears the latest wave of violence will threaten the country's second presidential election, which is being held in two weeks.
James Bays, Al Jazeera's correspondent in Kabul, said up to 700 polling stations may not open because of the ongoing violence.
"The Taliban have said they are going to disrupt the elections. We are just going to have to see in two weeks' time how many people are going to defy that," he said.
The bomb blasts came on the first visit to the country by Anders Fogh Rasmussen, Nato's new secretary general, who has said Afghanistan is a top priority for the military alliance.
|Thousands of Nato troops are conducting offensives in Helmand [AFP]
Rasmussen, a former Danish prime minister, vowed to strengthen military efforts to defeat the Taliban and other fighters as he arrived in the country.
"There is no alternative whatsoever to continued and strengthened military efforts," he said after talks with Hamid Karzai, Afghanistan's president.
Earlier he said that "pragmatic steps" were needed to improve Afghan security, adding that could include talking with anti-government groups.
The Nato leader will hold a series of meetings on Thursday, including with some of the 41 candidates for the presidential elections, for which Karzai is the frontrunner.
Thousands of Nato troops are conducting offensives in Helmand an area where roadside bombs are frequently used to attack foreign and Afghan forces.
Bays said international forces had stepped up their operations in recent weeks.
"In Helmand, there have been intensified operations by international troops, both the British and American offensives have been going on in the last month," he said.
Attacks on security forces have increased as Afghans gear up for a presidential election scheduled for August 20.
However, the attacks have come mainly in the south where Taliban fighters have their strongest presence.