Haroon Zarghon, the group’s spokesman, told the Times that the bombing was carried out by a 24-year-old who grew up south of Kabul.
More than 30 Afghan civilians were also wounded in the bombing, the Times reports.
It was the first major strike against U.S. and coalition targets inside the Afghan capitol in several months.
In February, Taliban gunmen and suicide bombers launched a string of attacks against the headquarters of Afghanistan's intelligence services in Kabul and in Jalalabad in the north.
Earlier this year, U.S. and coalition commanders warned that singular strikes on high-profile targets like Thursday's attack would be the hallmark of this year's fighting season in Afghanistan.
On Tuesday, four American soldiers were killed in southern Afghanistan when their convoy was hit by a massive roadside bomb when traveling through the Zhari district in Kandahar province, according to recent reports.
The Kandahar attack took place a day after insurgents detonated a truck bomb outside a NATO base Musa Qala district in Helmand province.
The three NATO soldiers based in a unit from Georgia were killed in the Musa Qala strike.
The string of attacks marks an early start to this springs' fighting season in Afghanistan, which will likely be the final fighting season for American troops in the more than decade-long conflict.
The American and NATO strategy for this year's fighting season is focused on flushing out Afghan insurgents from the so-called Pashtun heartland of the Taliban -- a swath of territory stretching north from southwest Afghanistan into the eastern part of the country along the Afghan-Pakistan border.
Thursday's attack in Kabul comes as Chairman of the Joint Chiefs of Staff Gen. Martin Dempsey wrapped up a two-day conference with NATO generals on the coalition's postwar plan for Afghanistan.
"It is still harvest season in Afghanistan, and I suspect we've not seen the height of this year's offensive," Dempsey told reporters while returning from the conference at the alliance's headquarters in Brussels.
"But this year, unlike years past, the offensive will be aimed at the [Afghan National Security Forces] not us, because, again, the Afghans will be in the lead," the four-star general said.
American units in the country during this fighting season will take a back seat to ANSF units in combat operations this spring, as U.S. troops prepare to pull out of Afghanistan next year.
Roughly 66,000 American troops remain in Afghanistan, with half of those forces scheduled to withdraw from the country this spring.
The final 32,000 American forces remaining in the country will start coming home following the country's presidential election in April 2014 — officially ending America's combat role.