Five employees of the ministry of mines and petroleum were killed and 10 wounded in the bus attack, the officials said, adding that seven people were killed and more than 20 wounded in the second explosion.
The rush-hour explosion sent a plume of smoke into the air above the Puli Mahmood Khan neighbourhood of the Afghan capital and shook buildings up to two kilometres (1.2 miles) away, with the media reporter saying he could hear gunshots after the blast.
The violence came on the first day of campaigning for the upcoming presidential elections, serving as a grim reminder of Afghanistan's woeful security situation and the sort of mayhem and murder that have beset previous polls.
A plume of smoke rose over central Kabul shortly after midnight and sirens could be heard. Inside the embassy, employees heard this message over the loudspeaker: "An explosion caused by a rocket has occurred on compound."
Green Village is separate from the nearby Green Zone, a walled-off and heavily fortified part of Kabul that is home to several embassies including the US and British facilities.
The death toll from a late-night Taliban suicide attack in the Afghan capital rose to 16 civilians on Tuesday, with 119 people wounded, an official said.
Fawad Aman, deputy spokesman for the Afghan Defense Ministry also says three other soldiers were wounded in Thursday's attack in the Chahar Asyab district in Kabul province.
Afghanistan has been witnessing a serious escalation in violence especially targeting innocent civilians and this has to end. The capital Kabul has been rocked by back-to-back bombings
The Ministry of Foreign Affairs and International Cooperation said in a statement that the attack, the second to take place this week for which the Taliban has claimed responsibility, represents an unacceptable escalation of violence and a heinous terrorist act against civilians and their families.
Strictly patriarchal Afghanistan has long been one of the world's worst places for women, but for a relatively small group — mainly in urban cores like Kabul — key freedoms such as education and the right to work proliferated after the Taliban fell in 2001.