A Lufthansa Airbus A340-600, registration D-AIHH performing flight LH-520 from Munich (Germany) to Mexico City (Mexico), landed on Mexico City's runway 05L but burst 4 main tyres during roll out. While the aircraft taxied towards the apron smoke emanated from the landing gear prompting the crew to declare Mayday reporting "we have fire on the aircraft, we need the fire brigade". Emergency services responded and sprayed the landing gear, the passengers were kept on board while emergency services were working. A passenger reported the aircraft touched down very hard, rolled out and vacated the runway when the aircraft stopped. The captain told passengers that the brakes needed to be cooled, smoke was seen from the landing gear area. The passengers were re-briefed on the procedures for a possible evacuation. After emergency services had arrived and dealt with the situation, passengers disembarked onto the taxiway via stairs as the aircraft was disabled, it was hinted to the passengers that a tyre had come off. The airline reported that 4 main tyres had blown during braking activity. The occurrence aircraft remained on the ground in Mexico for 3 days, then positioned to Munich and remained on the ground in Munich for another 3 days before returning to service.