At least 40 heavily armed police officers guarded the church in the northwest of the city as Prime Minister Helle Thorning-Schmidt joined the mourners to bid farewell to 55-year-old Finn Noergaard.
Danish police told AFP 750 people attended the ceremony, correcting an organiser's previous estimate of 1,200. Among the attendees were Muslim and Jewish leaders in Denmark.
Noergaard was shot dead outside a cultural centre on February 14 during a seminar on free speech and Islam in the first of two attacks by a gunman who also killed a Jewish man outside a synagogue.
The Jyllands-Posten newspaper reported witness accounts that Noergaard had tried to intervene as the gunman -- named by police as Omar El-Hussein, a Dane of Palestinian origin -- fired off dozens of bullets at the cultural centre.
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"We do not know what Finn was thinking in that situation, but we are sure that it was not his own security but that of others he was concerned about," Noergaard's two sisters wrote in a letter published in several Danish newspapers.
Known primarily for making documentaries, Noergaard had a special interest in the problems of integration. One of his best known works, however, was a 2004 film about a young Australian boomerang thrower.