
Joel Ortega, the city's chief of police, said that people turning in smaller guns could opt for an Xbox 360 or cash payment, and those giving up high calibre weapons could receive a computer.
Ortega promised no repercussions in the weapons amnesty, and stressed that the owners' anonymity will be protected.
The initial focus will be in the barrio of Tepito, a section of the city infamous for its flea markets selling pirated goods.
A total of 17 guns were handed in on Tuesday, 12 of which came from Tepito.
Mexico City police have made 100 computers available, complete with software donated by Microsoft, for the first wave of the programme.
The initiative will soon be extended to Iztapalapa, another of the city's trouble spots, according to newly elected mayor Marcelo Ebrard.
The surrendered guns will be destroyed by the Army.