"We had no people the past night who were not allowed to travel or caused problems," he said.
Kaliningrad is one of the Russian cities hosting World Cup matches, and the final group match between Belgium and England will take place there on Thursday night.
Football fans with Fan IDs can travel by train from mainland Russia to Kaliningrad and back free of charge. They cross the Lithuanian territory during this trip, and Lithuanian officers have stepped up border control.
Officials are concerned that fans from poorer countries might take advantage of free train rides through the Russian territory to eventually reach the European Union.