In a new, $15 million U.S. advertising campaign to promote tourism, Mexico calls itself "the amigo country," a land where "the colors haven't faded, the excitement hasn't lessened . . . and the fun hasn't stopped for over 2,000 years."

If successful, the campaign will help resolve what the Mexicans see as a growing image problem - the perception of their country as a land where an American visitor is more likely to be accosted by "bandidos" that welcomed by "amigos."

Sixteen Americans were murdered in Mexico last year. Two others disappeared, and have not been heard from since. In the past seven months, more than 20 American tourists have reported assaults and robberies, primarily by highway gangs in the north-western state of Sinaloa, where many lost everything from their automobiles to the clothes they were wearing.

To the consternation of Mexican officials trying to reassure frightened potential tourists, most of those incidents have been reported in detail by the American press.

Taken in context - with more than 3 million Americans visiting Mexico in a peak year - the numbers are hardly significant. As Mexicans are fond of pointing out, more than 1,000 New Yorkers are murdered yearly without leaving home.

While the total number of murders has remained the same in each of the past four years, robberies and assaults have increased significantly in recent months. The amount of what the State Department calls "open banditry" has been enough for it to warn tourists of " serious danger in motor travel in Sinaloa." The American Automobile Association has advised its members to stay out of the state, which includes large tourist areas such as Mazatlan and Culiacan.

The "bandido" stories, and the publicity they have generated in the United States, have spread a pall over American enthusiasm for south-of-the-border travel, and provoked both anxiety and occasional outrage in the new government of Mexican President Jose Lopez Portillo.

The Mexicans say that they have stepped up highway police patrols and warned tourists to stay out of certain remote areas where they admit to problems with what the National Tourist Council coordinator, Gen. Miguel Guarjardo, calls "groups that would like to see Mexico get further away from the United States."

But Mexico clearly feels that the American press and bureaucracy are making a mountain of danger out of a molehill of scattered experiences that add up only to normal travel risks. While Mexicans are taking pains not to upset thawing economic and diplomatic relationships between the new Carter and Lopez Portillo presidencies, there is an undercurrent of objection to the way the unpleasant incidents are reported.

Guarjardo particularly objects to what he calls "refrito" - refried - news stories that he feels unnecessarily recount the gory details of past incidents of banditry everytime a new one occurs.

A travel article referring to the safety problem and recalling several of the more recent incidents appeared in the Jan. 9 edition of The Washington Post. On Jan. 10, an article in the Mexican paper Novedades said The Post had printed a collection of articles "against" Mexico, and "showing Mexico with few actual tourism possibilities." An additional Mexican press report raised the same objections to a recent New York Times article on the assault problem.

Mexico has every reason to be upset over a potential loss in tourism. With unemployment at 15 per cent, and underemployment estimated at nearly 40 per cent, it means a loss of precious jobs.

Perhaps even more important, Mexico hopes to make $3 billion from tourists - primarily Americans - this year, according to Guarjardo. The country is heavily in debt, and the tourist industry supplies as much as 46 per cent Mexico's total dollar earnings.

Lopez Portillo took office last December at the end of one of the worst tourist years in Mexico's recent history. Beginning with a 7 per cent decline in the last half of 1975, blamed on worldwide recession, the number of American visitors dropped 20 per cent in 1976 following a Jewish boycott brought on by former President Luis Echeverria's support of a U.N. resolution equating Zionism with racism.

Reports of mistreatment of American prisoners in Mexican jails, gun-and narcotics-running, and land take-overs by peasants did not help matters.

Lopez Portilla, in the first weeks of his administration, declared the revitalization of tourism one of its highest priorities. The cost of the new advertising campaign, conducted through a New York agency and scheduled to begin next month, is double last year's budget. An American public relations firm is organizing free "fam" (familiarization) trips for newspaper and magazine writers.

A committee of the American Jewish Congress is just back from a trip - made at Lopez Portillo's invitation - to gauge Mexican anti-Semitism. The committee said it found none. The group plans to resume its Mexican travel packages this fall. Jewish leaders also lunched with Mexico's first lady, Romana Lopez Portillo, during her visit here for President Carter's inauguration.

"Our attitude," said Jewish Congress spokesman Richard Cohen. "will greatly influence all American Jews."

In fact, relations between Mexico and nearly all segments of American society are better than they have been for several years, with Lopez Portillo scheduled next month to be the first foreign head of state to meet here with Carter. The fact that the tourist problem seems to be the only thorn in an otherwise rosy picture makes it all the more irritating to the Mexicans.

Guarjardo said he has patience. "It is understandable that the issues of the past administration [Echeverria's] are still with us," he said.Americans "have not had a chance to understand the change that is taking place in Mexico. The business, the bankers - they understand. It is going to take time."

There are those on this side of the Rio Grande, however, who think the Mexicans are missing the point and making a basic misjudgment about what it will take to reassure American tourists that Mexico is safe.

While the safety issue has been discussed on a diplomatic level, one U.S. official said, and the Mexicans have made assurances about increased highway patrols, the Mexicans "still have tended to place more emphasis on public relations to minimize the seriousness of the problem," the official said. "They are still trying to solve it with words."

When American Automobile Association President J. B. Creal wrote to Lopez Portillo to "state our concern and ask his assurances that Mexico will do everything possible to prevent problems," an association spokesman said, he also included a note of congratulations on the new Mexican president's inauguration.

The Mexican response, more than a month later, was a one-sentence telegram: "Am very grateful for your congratulations on assuming the office of President of Mexico."

One American woman, who considered her safety "assured" by the Mexican government, decided several weeks ago to make an automobile trip through Mexico.

According to Julia Roe, 38, a Los Angeles resident, she and her fiance, J. Ramon Garcia, were driving near Culiacan on the evening of Jan. 5, when they were forced off the road by two bandits and ordered to drive into the country. When they resisted, she said, Garcia was shot four times and killed.

After several days of questioning by Mexican officials, Roe left the country with an armed guard. U.S. officials confirm her account.

Days before their trip, Roe said in an interview last week, she and Garcia had heard a Mexican official, in a television appearance with Los Angeles Mayor Thomas Bradley, say that Mexican highways were safe, that extra patrols had been added, and there was nothing to worry about.

"He lied about the situation there," Roe said of the minister. "We saw no police protection whatsoever all along the highway. It's open season on Americans down there. It's very dangerous . . . and everyone should be made aware of this."