MEXICO CITY, DEC. 9 -- An international consortium that includes Southwestern Bell will pay $1.76 billion for controlling interest in Mexico's telephone monopoly under a privatization program, the finance ministry announced today.

The winning bid of $2.03 a share will give the group 20.4 percent in Telefonos de Mexico (Telmex), a trouble-plagued system operating about 4.1 million telephones.

In addition to St. Louis-based Southwestern Bell, the winning consortium included Mexico's Grupo Carso and France's Cable & Radio.

A bid of $1.69 billion was offered by a group made up of Acciones y Valores de Mexico, GTE Corp. of Stamford, Conn., and Telefonica de Espana. Mexico's Grupo Gentor had offered nearly $1.6 billion.

The government holds more than $4 billion worth of shares in the company, which is valued at about $8 billion. It plans to sell the remainder of its shares on national and international stock markets.

The winners are required to post guaranteed funds by Dec. 20.

President Carlos Salinas de Gortari in September 1989 announced plans to sell off Telmex as part of a program of privatization to help revive the national economy.

The effort seeks to improve phone service, expand the system and strengthen research and development.

Earlier today, three cabinet ministers signed documents to give Telmex workers 4.4 percent of the shares.

The shares are to be turned over to the workers within eight years, after a $325 million credit from the government is paid off, according to the government's Notimex news agency.

Telmex had launched a three-year modernization program to help make it more attractive to buyers.

The company in September signed $300 million worth of contracts with a group led by American Telephone & Telegraph Co. for a new optic-fiber cable network and terminals.

Poor service by Telmex, a state monopoly since the mid-1960s, has often been blamed for helping hold back economic development in the nation of about 84 million people.