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 Amé rica Mó vil and Spain's Telefó nica.

AT&T Chief Executive Randall Stephenson outlined the investment plans in a meeting with Mexican President Enrique Peñ a Nieto on Thursday.

"We are building a network in Mexico that is capable of bringing innovation and economic vitality to the country, just as we have done in the U.S.," Mr. Stephenson said, according to a release.

AT&T said it expects the network to reach 40 million people in the next six months and 75 million by the end of 2016.

AT&T's strategy for Mexico includes leveraging its U.S. network, which it will expand into a "North American Mobile Service Area" of 400 million potential consumers. Starting next month, AT&T's Mexican customers will be able to use their individual plans for voice, data and messaging while in the U.S. and will be able to call friends and family in the U.S. who are on the AT&T network, the company said.

"AT&T's interest [in Mexico] was piqued by the Mexican regulator's declaration of Amé rica Mó vil as a preponderant [dominant] telecom player and the advantages that have been given to smaller players since, as well as Amé rica Mó vil's clear willingness to cede subscribers from here to remove the preponderance label over time," analysts with J.P. Morgan said in a note to investors.

Its acquisitions in Mexico were "short on subscribers and scale, but with a lot of spectrum," they added.

The U.S. company reported six million subscribers at Iusacell at the end of March, after adjusting down the number from 9.2 million when it acquired the Mexican company in January. Nextel Mexico had around three million subscribers when AT&T bought it in April.

Amé rica Mó vil unit Telcel had 72.1 million wireless subscribers at the end of March, and Telefó nica had 22.5 million.

Write to Anthony Harrup at anthony.harrup@wsj.com

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