Mexican tycoon Carlos Slim plans to enter the online gaming market in his home country, offering more than 600 free titles to some 8 million users of his high-speed broadband for a month, with the aim of charging for the service afterward.

Slim's fixed-line company, Telmex, now a unit of cell phone giant America Movil, is the top provider of Internet services in Mexico. Its popular plan for computer purchases - payments are included in the phone bill - has largely helped to boost Internet use in the country.

Telmex said its premium Infinitum Games service will have a monthly cost of 99 pesos, or around $7.50. Most of the titles were developed by a U.S. gaming company.

This is Slim's latest move into content, as rising use of personal computers, tablets and smartphones in the country and the rest of Latin America prompts him to explore new markets.

Slim's Telcel, the commercial brand of America Movil in Mexico, recently stopped offering unlimited Internet access plans because consumer demand was so great that it hogged too much bandwidth on the network.

Last year, America Movil branched out by purchasing Miami-based DLA Inc, a digital media firm that distributes movies and television series from U.S. entertainment houses, as well as music to televisions and smartphones.

The world's richest man is also financing an Internet TV network that will include a show hosted by former CNN television host Larry King, who is a personal friend of Slim's. The venture could be running by October.

The government has blocked Slim's Telmex from offering television services in Mexico. But there are few other TV restrictions to his operations in Central and South America.

$1 = 13.18 Mexican pesos

(Reporting By Cyntia Barrera Diaz; editing by Matthew Lewis)