Gunfire erupted when four armed men stormed the building of the aid group Care in the Shar-e-Naw area following a car bomb explosion.
All attackers were killed. No group has admitted carrying out the attack, the fifth to hit the city in 24 hours.
Taliban militants, have increased their attacks in Kabul recently.
On Monday, a series of blasts claimed by the group hit a busy part of the city, close to the defence ministry building.
Officials now say, 35 people were killed, including an army general and four senior police officers. Some 103 others were wounded, they added.
The latest incident struck a prosperous business and residential area of Kabul, home to several guest houses and where many foreigners and diplomats live.
A government spokesman told the BBC that six other civilians were injured in the hours-long standoff.
Some 42 people were rescued during the operation, including 10 foreigners, he added.
Traffic was blocked in several parts of the city and schools were closed.
The recent attacks highlight the deteriorating security situation in Afghanistan, which has left dozens of civilians dead.