According to the ministry, a suicide bomber blew himself up at a roundabout close to the Marshal Fahim Military Academy.
No group immediately claimed responsibility for the dawn attack, which comes after almost three months of relative calm in the capital.
Past year at least six people were killed during a suicide bombing just outside the academy.
The agreement would call for the Taliban and US forces to refrain from conducting attacks or combat operations for seven days, according to a person familiar with the ongoing discussions who was not authorized to discuss the proposed agreement and spoke Tuesday only on condition of anonymity.
It is also being said that this attack took place at a time when the United States is trying to negotiate with the Taliban for a ceasefire in Afghanistan. Recent weeks have brought frequent attacks on police and US security forces in Afghanistan, even as the United States and Taliban Islamist militants pursue talks to finalize a peace pact.
Afghan President Ashraf Ghani condemned the attack in a statement released by his office. The Taliban and militants from the Islamic State group regularly target Afghan forces.
"The blast affected several people, including civilians and military personnel".
Pompeo last week demanded "demonstrable evidence" from the Taliban that it will lower the violence level in Afghanistan before signing a deal that would lead to peace talks and a withdrawal of American troops from the country.
Tuesday's blast comes as Washington and the Taliban wrangle over a possible deal that would see USA troops begin to leave Afghanistan in return for security guarantees.
Four foreign nationals were among the wounded.
"The Secretary informed me about the Taliban's proposal with regards to bringing a significant and enduring reduction in violence", Ghani wrote without providing specifics.
Talks were restarted in December in Qatar, but paused again following an attack near the US-run Bagram military base in Afghanistan.
A reduction in violence would allow the USA and Taliban to sign a final agreement, prepare the way for ending America's longest war and for starting broader Afghan negotiations over the country's post-war future.
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