MEXICO CITY—AT&T Inc. plans to invest around $3 billion in Mexico to make its high-speed mobile Internet service available to 100 million people by the end of 2018, the U.S. telecommunications company said Thursday.

AT&T has spent about $4.4 billion this year in acquiring Mexican mobile company Grupo Iusacell and NII Holdings Inc. unit Nextel Mexico, setting up a beachhead in the country from which it plans to step up competition for billionaire Carlos Slim’s telecoms company América Móvil and Spain’s Telefónica.

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