In the wake of the tragic earthquake that struck Mexico City Sept. 19, the Mexican government has begun an urgent campaign to reassure U.S. tourists about their safety and protect its vital high season winter travel business.

Officials in Mexico emphasize that the extensive destruction was confined to a relatively small, older section of the city -- primarily Colonia Roma, but also affecting parts of downtown and the Zona Rosa, a major tourist area. Power, water, sewage, transportation and local phone systems in the capital are now operating, all 53 airports around the country are handling traffic, and all highways are open. The initial quake and aftershock left major tropical resorts like Acapulco and Cancu'n unharmed.

More than 8,000 bodies have been recovered from the wreckage in Mexico City (10 Americans are known dead and 15 are unaccounted for, according to the State Department) and thousands of Mexicans are still missing. More than 400 buildings collapsed, about 300 are believed ready to fall and some already have been torn down. Damages are estimated at $4 billion. These figures have triggered vacationers' fears about the possibility of another violent quake.

Travel agents on both sides of the border have been concerned that the tragedy in the capital might cause many Americans and others to bypass -- at least for a time -- that center of culture, business and government. (The city is the main destination for tourists, who generally combine it with one of the beach resorts as part of a package.) Or worse, since some people refer to Mexico City as "Mexico" for short, geographically confused travelers might mistakenly cross the entire country off their winter vacation lists.

The capital is a major airline gateway -- though not the only one -- to the popular recreational, historical and archeological sites scattered throughout the country that last year drew nearly 5 million visitors. Almost 1 million stopped in Mexico City at least for a few days.

For Mexico, already suffering from serious inflation, high unemployment and a continuing flight of capital to the United States, the $2.2 billion tourism industry is second only to oil as a producer of much-needed hard currency. A sharp drop in arrivals from the United States, which supplies 85 percent of the visitors, would be another blow to its shaky economy even as the country begins the long process of restoration.

With these sobering facts in mind, tourism minister Antonio Enriquez Savignac flew to New York City recently with a message for travel industry leaders: "Many of the television reports . . . tend to give the impression that the capital was completely devastated. That impression is incorrect."

And as Mexico launched its advertising and public relations offensive, a group of U.S. tour operators returned to their desks from a one-week inspection trip to the capital and three resort cities.

"This is a slower fall season than normal, but people are still traveling to Mexico," said Anna Di Leo of Alexander Charters and Tours, a New York wholesaler/retailer specializing in packages to Mexico. She viewed conditions in the capital, inspected the minor damage in Ixtapa, and then stopped in Acapulco on the special tour. Other agents also visited Puerto Vallarta.

"We're getting a lot of bookings from agents" for the winter season beginning Dec. 15," Di Leo said. "Mexico City is not a dangerous area to visit."

At Gogo Tours in Paramus, N.J., which earned Mexico's "top producer" award last year for booking more tourists than any other operator, officials were concerned about a credibility gap. "The amount of damage is minimal -- but how do you tell this story to consumers and get them to believe it?" asks Steve Heydt, senior vice president for sales and marketing. "We would not be selling Mexico City and other areas unless we knew they were safe," he emphasizes. Gogo representatives recently conducted their own independent inspection trip.

"Unlike certain islands in the Caribbean, airline and hotel space in Mexico is still available for Christmas and other peak periods," Heydt says.

Mexico was not enjoying a super season before the earthquake, although business was increasing. That was because its hotel rates and airline fares -- despite some earlier benefits from devaluation -- could not compete effectively with European prices due to the strong dollar abroad, Heydt says. "Our advance winter bookings are not as strong as they were this time last year."

Full restoration of international phone service and normalization of communications with the rest of Mexico were expected momentarily. Earlier, to enable members of the travel industry to communicate with hotels, tour operators and airlines in Mexico, the government set up an air courier service from New York.

Pan American, American, Eastern, Mexicana and Aeromexico are the five major airlines flying between the two countries. All agree their traffic is down, though load factors may vary depending on the U.S. departure point; but some lines report good business to Cancu'n in the Yucata'n. "Our bookings are wide open," according to an American Airlines spokesman. Eastern was faced with an additional problem Oct. 10, when all its flights to Mexico were canceled by a strike of its Mexican ground personnel. Talks with the union were continuing last week.

Here is a summary of current conditions affecting visitors to Mexico City, according to a government-sponsored survey:

HOTELS: Of the capital's 507 hotels with a total of 35,350 rooms, 153 hotels with 19,167 rooms were located in the areas hit by the tremors. Six hotels with 888 rooms were totally destroyed, andseven with 848 rooms were partially destroyed and probably will not be restored. Twenty-two hotels suffered major damages, 25 have minor damages, 51 have decorative damages such as fallen plaster, and 42 hotels remain in perfect condition.

While 9 percent -- 1,736 -- of all hotel rooms in the capital have been permanently wiped out, the majority of the country's 250,000 hotel rooms were unaffected. Mexico City hotels destroyed were: the Regis, Principado, Finisterra, Romano Downtown, Versailles and Central; the Continental, De Carlo, Residencia and Montreal were among those "semi-destroyed." Among well-known properties listed as having received minor damage are the Alameda, Del Prado, Reforma, Del Paseo, Presidente (Zona Rosa) and Maria-Isabel Sheraton. (If you are considering booking a particular hotel, the best way to check its status is to contact a travel agent.)

HEALTH: The Pan American Health Organization said last week there is no danger of epidemics in the capital, and tourists do not need any vaccinations to visit any area of Mexico. The Mexican Ministry of Health has recommended that, as a precaution, visitors to the capital avoid drinking any water that has not been boiled or bottled -- a standard rule over the years for many tourists, especially in the tropics. The government also suggests that visitors avoid food and drinks sold on the capital's streets.

TOURIST ATTRACTIONS: The majority of Mexico City's attractions -- such as the Metropolitan Cathedral, National Palace, Palace of Fine Arts and the National University -- are reported to be in perfect condition, but in some cases tour operators have had to modify routes because some areas are cordoned off. The internationally famous National Museum of Anthropology in Chapu'ltepec Park also escaped unscathed.

Among places damaged but restorable are the well-known typical tourist zones: La Lagunilla, La Merced, Tepito, Plaza Garibaldi and Zona Rosa. The only archeological zone affected was the Ehecatl Temple in the Pino Suarez subway station. All nonhotel bars and nightclubs were untouched. Of 354 restaurants belonging to the Mexican Restaurant Association, only 12 incurred damages that forced them to close.

OTHER TOURIST AREAS: Ixtapa/Zihuatanejo on the Pacific coast was the only major resort area to suffer damages from the tremors of Sept. 19 and 20. They were mainly superficial and affected only the buildings' masonry and external surfaces, according to the town officials. Three of the 28 hotels in the area remain closed.

Club Med-Ixtapa was undamaged but will be closed until Nov. 15 to permit a thorough inspection. Three other Club Med Mexican resort villages -- at Playa Blanca, Guaymas and Cancu'n -- were untouched and remain open. Also undamaged and open are the Club's five archeological villages -- three in the Yucata'n and two outside Mexico City at Teotihuaca'n and Cholula.

The Mexican Ministry of Tourism has been providing travel agents with daily updates on conditions within the country through its New York office. Vincent Hodgins, director general of operations in the United States and Canada, says tourists can obtain more information from their agents, or contact the Mexican Tourism Office, 405 Park Ave., Suite 1002, New York, N.Y. 10022, (212) 755-7261.