Carlos Gonzalez said Alfredo David, 20, and Diego Alejandro Paramo Gonzalez, 21, were killed Sunday as they traveled through Chihuahua's city's Arboledas district, the Latin American Herald Tribune reported.
They were the sons of Martha Nicholson, publisher of the daily newspaper El Peso and David Paramo, a business reporter for a Mexico City newspaper, but the killings were not linked to their parents' professional activities, Gonzalez said.
The prosecutor's office said a motive hadn't been determined, El Universal reported.
The young men were killed two days after Mexico observed World Press Freedom Day.
Media rights groups have reported a rise in threats and attacks on journalists in Mexico.
The Mexican National Human Rights Commission said 84 journalists have been killed in the country since 2000.