MCI Communications Corp. spread its long-distance network across 79 more countries last month, part of the Washington-based company's efforts to match the service level of American Telephone & Telegraph Co. in foreign as well as domestic markets.

The additions bring to 146 the number of nations that MCI customers can dial direct -- the same number of countries that AT&T customers can dial direct. MCI says its rates on the average are lower than AT&T's.

Among the countries added were Mexico and West Germany, two high-volume markets for American callers. But for the most part, the new countries have little telecommunications traffic and aren't expected to bring MCI a lot of money through extra call billings.

Rather, analysts saw the move as part of a larger effort by MCI to raise sales by expanding its corporate customer base. "They've got to be able to serve everywhere to be able to attract the large business market," said Daniel Zinsser, a vice president at Goldman Sachs & Co. who watches the telecommunications industry.

MCI already has about 8 percent to 10 percent of the United States' $5 billion- to $6 billion-a-year business in overseas calls. Aided by the emerging integration of the world economy and declining rates, the international market has been expanding faster than domestic long-distance traffic. MCI has estimated the growth at 15 percent to 20 percent a year. AT&T, which controls most of the market, has said growth is slower than that.

MCI has been investing heavily to install its own hardware for the world network, which handles both voice and data traffic and, in the company's view, is the most versatile available in the U.S. In 1982, it paid $195 million to acquire Western Union International, which had extensive telex and data facilities. MCI has shares in all cables under the Atlantic and Pacific oceans now in operation or being built. It has acquired an earth station for satellite transmission and is building a second for itself.

But to add 79 countries in one stroke, the company has had to rely in some cases on a strategy it used in building its domestic network -- riding on the shoulders of its rival, AT&T. For some countries, it is leasing lines from AT&T until it has the resources to build its own. MCI plans to add six to 12 of those countries to its own network this year.

MCI also is putting in place an operator network that will enable customers to reach countries that are not on other companies' direct-dial networks.

Meanwhile, U.S. Sprint Communications Co., the nation's third-ranked long-distance company, is proceeding with similar plans to match AT&T's service level. Last week, it announced plans to expand beyond the 70 countries now on its network to reach almost all of AT&T's 146, though it did not give a precise timetable for reaching that goal.

In the first quarter of 1988, Sprint will open service to a group of nations that includes West Germany, Greece, Switzerland and Israel. Like MCI, it is using both its own lines and ones leased from AT&T.

Overseas rates have been falling for years, due more to deregulation than to new technology. AT&T says that a 10-minute call to London that cost $22.50 10 years ago can now be made during the evening discount hours for $9.39. In the old days, there were no time-of-day discounts for international calls.

Despite the price declines, the international business remains more profitable than domestic long distance. But that gap could narrow or disappear. Jack Grubman, telecommunications analyst at PaineWebber Inc., suggests that the new entrants will accelerate the downward trend of rates. "AT&T will do internationally what it's done everywhere else when competition starts up, which is cut rates," he said.

AT&T suggests that it is not too concerned about MCI's new move. Ray Butkus, deputy director for international marketing, said AT&T still offers a wider variety of services than MCI, even if the number of countries reached by direct dial is the same. AT&T has about 180 employees assigned to 24 countries, he said. It offers special services, such as discounts on the surcharges many hotels put on overseas calls.

While trying to wrestle away each other's market share, the companies are also trying to expand the total pie. In advertising, they are stressing the ease of direct-dialing, even though in some cases customers will find it means little -- calls will fail to go through at the other end, particularly if they are to developing countries.

Many business users have come to see overseas calls as little different from domestic long distance and don't hesitate to pick up the phone. But for ordinary people calling from home, who make up about half of AT&T's customers but only a small portion of MCI's, old attitudes linger.

MCI is fighting back. "We still have to ... convince them that it is no longer a monumental affair that requires the dog, the cat and the whole family around the phone at the same time," said Seth D. Blumenfeld, president of MCI International, which handles MCI's overseas operations.

AT&T is busy, too. In a variation on its time-tested "reach out and touch someone" campaign in the domestic market, AT&T ads are now advising people to "surprise someone in Sapporo."