Classes resumed Tuesday after two days of orientation, Zubaida Akbar, head of media at the university, told CNN.
The 13 killed included seven students, three police officers, two security guards and a doorman. Thirty students were injured in the attack, for which no group has claimed responsibility.
"We are so happy today... Such deadly attacks cannot prevent us from gaining knowledge. We will continue going to university at any cost," said Ahmad, a political science student.
"I hope terrorists do not target education centers in the future, as these places are for knowledge, not for doing such attacks," the student, who declined to be fully named for security reasons.
Two gunmen were killed after police entered a building hours after the shooting started, and a third attacker was killed when he detonated an explosives-laden car in front of the university wall, Mujahid said.
The gunmen detonated explosives and fired guns, witnesses said, causing some students and faculty to flee. Others hid inside buildings, a senior US State Department official told CNN last August.
Despite the name of the school, few Americans study there, a senior State Department official said, though a number of Americans are on the faculty. The school is regarded as a symbol of cooperation between Afghanistan and the United States.