MEXICO CITY (AP) _ The new owners of Mexico's phone system have promised to double the size of the company within six years.

A consortium including St. Louis-based Southwestern Bell, France Cable & Radio and Mexico's Grupo Carso conglomerate is buying a controlling interest in Telefonos de Mexico, the state-owned telephone company, for $1.76 billion.

Grupo Carso is the lead partner and will run the newly privatized Telmex.

''We promise the investment and effort necessary to grow rapidly, 12 percent a year, a rate that means the size of the company will double in six years,'' Grupo Carso President Carlos Slim said Tuesday.

He said the number of public telephones would be quadrupled in four years and every village with at least 500 residents would have access to a telephone by 1994.

The emphasis, he said, will be on expanding and modernizing the service by investing ''at the most intense rhythm possible.''

Digital equipment, mobile telephones, better support services for major clients and decentralization are top priority, he said.

But it will take time, he warned, to give Mexico a truly modern, efficient telephone system.

''One must have patience,'' he said.

Slim also said the new owners will do their ''utmost to avoid reducing personnel and instead train them for new jobs that modernization will demand.''

Telmex, which now provides only about 5 million lines to this nation of more than 80 million people, has 50,000 people on its payroll.

Union opposition to the privatization eased somewhat after the government agreed to provide $325 million in financing so the employees can buy stock representing 4.4 percent of Telmex.

In addition, the government plans to sell Telmex stock on the Mexican and international stock exchanges.

Slim said the resources, experience and technical expertise of Southwestern Bell and France Cable & Radio will be important to Telmex's success

Even though the foreign partners will not play a role in administering Telmex, they will have a decision-making role.

The privatization of Telmex is a centerpiece of President Carlos Salinas de Gortari's campaign to modernize Mexico's economy and attract foreign investment.