Federal prosecutor Peter Frank told reporters that there were many open questions in the probe into Tunisian national Anis Amri, the suspect who was killed when he opened fire on Italian police in Milan.
"It is very important for us to determine whether there was a network of accomplices... In the preparation or the execution of the attack, or the flight of the suspect," he said.
Interior Minister Thomas de Maiziere later thanked Italian police for their swift action, saying the officers had been "especially brave" and done "excellent work".
"I am very relieved that this attacker no longer poses a threat," he said, adding that a team of German federal police were bound for Italy to assist in the probe.
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He said the case demonstrated "the enormous importance of European and transatlantic cooperation in the fight against terror".
Federal police chief Holger Muench said that "hundreds of investigators" would be working on the case "despite the Christmas holidays" beginning tomorrow.
Amri, 24, was suspected of killing 12 people and wounding dozens more in Monday's assault on the Christmas market, which has been claimed by the Islamic State jihadist group.
Italy's interior minister Marco Minniti told reporters in Rome that Amri had been fatally shot after pulling out a pistol and firing at police who had stopped him for a routine identity check around 3:00 am (local time) near Milan's Sesto San Giovanni train station.