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Kabul, Afghanistan (CNN) -- Suicide bombers struck at targets in Kabul and Afghanistan's eastern Kunar province on Tuesday, killing 13 people and wounding 15 others, including three NATO soldiers, Afghan officials said.
Taliban groups took responsibility for both attacks.
In the first one, a 22-year-old woman named Fatima drove a car packed with 660 pounds (300 kilograms) of explosives into a van on a road leading to Kabul International Airport, according to Hezb-e-Islami Gulbuddin, a group allied with the Taliban that took responsibility for the attack.
The blast killed 12 people and wounded 11 others, government officials said.
Video footage of the aftermath showed a charred vehicle smoldering on the road as military officials milled about the blast site.
Eight of the dead were South Africans, a government spokesman confirmed, all working for an international flight provider, some of them as pilots.
Three of the dead were Afghan civilians, and another was a citizen of Kyrgyzstan, Afghan President Hamid Karzai's office said.
Hezb-e-Islami Gulbuddin said the attack was revenge for an anti-Islam film that has angered the Muslim world.
The South Africans were ethnic Caucasians, said Clayson Monyela from South Africa's International Relations Department, who suggested they could have been mistaken for Westerners associated with U.S. or NATO military powers.
South Africa not only has no troops in Afghanistan but also has no consulate or embassy, Monyela said.
The International Relations Department issued a statement saying it was working to confirm the identities of the dead and notify their relatives.
Karzai condemned the attacks, saying in a statement that those behind it were "thirsty of blood" and an "enemy of mankind."
The U.S. Embassy in Kabul also condemned the attack.
"This vicious attack again shows that the insurgents have no respect for human life," the embassy said.
In Kunar province, the Taliban claimed responsibility for a suicide attack that killed an Afghan civilian and wounded four people, including three International Security Assistance Force troops, according to Wasifullah Wasifi, a spokesman for the provincial governor's office.
They were working on a bridge repair project, Wasifi said.
Lt. Col. Hagen Messer, spokesman for the NATO-led force, confirmed the incident and that NATO troops had been injured.
The use of a female car bomber in the Kabul attack is an anomaly in Afghanistan, where women are usually not allowed to drive, and may highlight a recent increase in the use of tactics by the Taliban to avoid detection beforehand.
Afghan insurgents who staged a daring, well-planned raid Friday on Camp Bastion, the military base where Britain's Prince Harry is serving, were wearing U.S. Army uniforms.
It's rare for Afghan insurgents to don U.S. uniforms for their attacks. The last time CNN can identify the tactic was in August 2010 when NATO repelled attacks on two bases in Khost province.
Though seldom used, such tactics are not new to the Taliban, said documentary filmmaker Mehran Bozorghmia, who has filmed the Taliban. "These sort of plannings were going on three years ago."
Recent green-on-blue attacks, in which Afghan army troops open fire on allied International Security Assistance Force soldiers, represent yet another cloaking tactic in the Islamist militia's clandestine game, Bozorghmia says. The Taliban "have sleepers inside the army."
Such insiders could have also gained access to the U.S. Army uniforms that insurgents wore in Friday's attack.
Tuesday's attack is another violent response to an online film, produced in the United States, that mocks Islam's holy prophet. Protests started last week, including an attack at the U.S. Consulate in Benghazi, Libya, that killed Ambassador Chris Stevens and three other Americans.
Washington has made it clear it did not sanction the low-budget, amateurish 14-minute movie trailer posted on YouTube and produced privately in the United States. The clip, which has been banned by YouTube in several countries, mocks the Prophet Mohammed as a womanizer, child molester and killer.
CNN's Anna Coren, Ben Brumfield and Esprit Smith contributed to this report.