President Andres Manuel Lopez Obrador was travelling outside Mexico City at the time.
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Preliminary reports indicated an armed man entered a building on a small street near the palace looking to relieve himself, city police said.
After two people in the building told him off, the man pulled out a pistol and opened fire. When police arrived, they found four people with gunshot wounds lying in the building’s courtyard, and shot at the gunman.
Paramedics found the gunman dead, along with two other people, the police said. One of three people who were injured died en route to hospital.
More than 100 police officers rapidly arrived and cordoned off the street, according to television images.
The building sits in a narrow, pedestrian-only street that opens onto an entrance of the National Palace used daily by government staff and reporters.
Lopez Obrador took office a year ago on promises to run a more austere government. In addition to cutting the president’s salary by half, he shed various trappings of power, including a large force of secret-service style bodyguards.
The leftist also turned the luxurious Los Pinos presidential residence into a cultural centre and moved into the centuries-old National Palace.
Firing near Mexico‘s presidential residence killed four people.