The brazen attacks were mounted after Obama left Kabul following a previously unannounced visit during which he signed a strategic partnership agreement with his Afghan counterpart Hamid Karzai.
"There were at least two suicide car bombings near a logistic camp named Green Village run by foreigners in Pul-i-Charkhi area this (Wednesday) morning," a police source told Xinhua.
He said the dead include a foreign security guard, five civilians and two suicide bombers.
Taliban has claimed responsibility for the attack that occurred at about 6.15 am.
At least 17 people were injured in the attack, a health official in Wazir Akbar Khan hospital told Xinhua, adding some of the injured were school children.
The area was cordoned off by security forces and police were on high alert across Kabul while several helicopters hovered over the area.
Obama signed a cooperation agreement with Afghanistan as he paid an unannounced visit to the war-torn country Tuesday.
"Afghanistan has a friend and a partner in the United States," said Obama before he and Karzai signed the Strategic Partnership Agreement outlining cooperation between their countries once the US-led international force withdraws in 2014, CNN reported.
Obama, on his third trip to Afghanistan since taking office, also addressed troops at Bagram Air Field.
During the signing ceremony, the US president said neither country asked for the war which began over a decade earlier, but now they would work in partnership for a peaceful future.
Addressing concerns in Afghanistan that the US would abandon the country once its troops leave, Obama said: "With this agreement, I am confident that the Afghan people will understand that the United States will stand by them."
"We came here with a very clear mission to destroy Al Qaeda," he said as the day marked a year after Osama was gunned down by US commandos in Pakistan's Abbottabad town.
Obama's visit to Afghanistan came a week after the Afghan and US governments finalised the US-Afghan strategic pact's draft.
The agreement, which paves the way for long-term US military presence in Afghanistan after the withdrawal of the NATO-led coalition force from the country by 2014, has been welcomed by local analysts as a security stabilising factor in Afghanistan.
At present, there are over 90,000 US troops in Afghanistan and the US is expected to draw down that number to 65,000 by the end of 2012 and to less than 20,000 by the end of 2014.