German Foreign Minister Frank-Walter Steinmeier said the suicide attack - the first to hit Kabul this year - was a "cowardly act" that would not deter Berlin.
Germany has 3,200 troops in Afghanistan, mainly in the country's north.
The heavily-guarded US base is the headquarters for soldiers training Afghan police and army forces.
Reuters news agency reported that Afghan relatives of the dead had gathered screaming and crying outside a nearby hospital.
Despite the heavy security in the district, which houses many embassies and offices of international organisations, the district has been attacked before.
In November four Afghans were killed by a suicide bomber outside the US embassy.
In Saturday's second attack, a suicide bomber killed a civilian while attempting to ram his vehicle into a convoy of Nato troops and Afghan police in Chaparhar district, Nangarhar province.
A Taleban spokesman, Zabiullah Mujahid, told AP news agency a suicide bomber had carried out the Kabul attack in a Toyota Corolla. The militant group later claimed the second blast too.
The militants' influence has spread from their traditional heartlands in the south and east to areas closer to the capital.
But the BBC's Martin Patience says that with increased police checkpoints throughout the city, there were fewer attacks inside Kabul in 2008 than in the previous year.
US President-elect Barack Obama has pledged to make Afghanistan a foreign policy priority after he comes to office on Tuesday and is expected to approve the doubling of US troops in the country from the 30,000 at present.
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