Looking back on the 60 years he had known Joseph Ratzinger, Kasper said: "Those were very good conversations and meetings, and I have to say, I miss them now. Perhaps we can continue them in heaven."
After the service, Benedict's body was to be buried in the crypt of St Peter's Basilica.
Benedict XVI died at the Vatican on New Year's Eve at the age of 95. He had been lying in state in St Peter's Basilica since Monday so that the public could pay their respects.