The Taliban, who strongly opposed the agreement with the US, claimed responsibility for the early-morning twin blasts that targeted vehicles taking military employees to work in the capital.
"There have been two suicide attacks targeting buses carrying Afghan national army personnel," Farid Afzali, chief of the city's police investigation department, told AFP.
"Six military personnel and one civilian were killed in one attack, and 15 were injured. Four military personnel were injured in the other attack."
There were conflicting reports on whether the attackers were on foot or driving cars laden with explosives.
The Taliban claimed responsibility for both blasts and said at least 20 soldiers were killed, but the insurgents regularly exaggerate death tolls after attacks.
"This is a clear message to the stooge government that signed the slave pact, and we will step up our attacks after this," Taliban spokesman Zabihullah Mujahid told AFP.
Afghanistan and the United States on Tuesday signed the long-delayed bilateral security agreement (BSA) to allow about 10,000 US troops to stay in the country next year.
Hamid Karzai, who stood down as president on Monday, had refused to sign the deal in a dispute that underlined rocky Afghan-US relations over recent years.
US-led NATO combat operations in Afghanistan will finish at the end of this year, and the Taliban have launched a series of recent offensives that have severely tested Afghan soldiers and police.
NATO's follow-up mission, which will take over on January 1, will be made up of 9,800 US troops and about 3,000 soldiers from Germany, Italy and other member nations.
He said it provided "the necessary legal framework to carry out two critical missions after 2014: targeting the remnants of Al-Qaeda and training, advising, and assisting Afghan National Security Forces."
The Taliban have often targeted buses that take government and military personnel to work every morning in Kabul, despite efforts by security forces to provide protection for the vulnerable vehicles.
In July, eight military officers were killed in a similar attack on an air force bus in Kabul.
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