MEXICO CITY — Running a newspaper, radio station or television outlet in Mexico usually means relying on a single, powerful client that spends exorbitant sums on advertising with a simple warning: “I do not pay you to criticize me.”

That client is the government of Mexico.

President Enrique Peña Nieto’s administration has spent hundreds of millions of dollars a year in government money on advertising, creating what many Mexican media owners, executives and journalists call a presidential branding juggernaut capable of suppressing investigative articles, directing front pages and intimidating newsrooms that challenge it.

Despite vowing to regulate government publicity, Mr. Peña Nieto has spent more money on media advertising than any other president in Mexico’s history — nearly $2 billion in the past five years, according to government data compiled by Fundar, a transparency group. It found that his administration spent more than twice the generous media budget Mexican lawmakers allotted it for 2016 alone.

And that is just the federal money.

Leaders from all parties marshal hundreds of millions of dollars in state money for advertising each year, money they dole out to favored news outlets, Fundar calculated. According to the executives and editors involved in the negotiations, some government press secretaries openly demand positive coverage from news organizations before signing an advertising contract.