He strode confidently past military aides and reporters, paused briefly to stroke the large pregnant belly of a bronze Mayan fertility goddess, then drove off in a convoy surrounded by sirens and bodyguards.

The first time he had seen the statue, years ago in the sculptor's studio, he made that same gesture instinctively, and the artist blurted: "One day you will be president."

Jose Lopez Portillo has now been president of Mexico for five years, and the bronze statue of Ixchim stands in the garden of the official residence, a rambling turn-of-the-century home.

And still, before an important occasion, Lopez Portillo stops to rub Ixchim's swollen stomach for good luck. If the show of superstition seems contradictory for this erudite former law professor, it also illustrates the complexity of the man who has come calling on President Reagan -- with whom he is said to share personal warmth despite policy differences -- and who arrived here last night for his two-day visit. Renaissance Man

Mexico's political class was taken aback when Luis Echeverria picked his longtime friend and short-time finance minister "Pepe" Lopez Portillo, now 61, to succeed him in 1976 as the country's leader for the next six years.

They did not see him as one of them, this quintessentially intellectual man, brought up on French and Spanish thought, a philosopher, author and administrator who had become fairly prosperous in the days when he practiced law.

In Mexico, politics is largely the domain of old-time revolutionaries, their descendants and followers, a mix of opportunists and idealists. Its professional members must cajole their way through the institutional apparatus, and not unlike Soviet apparatchiks, often put up with years of obscure drudgery to earn their place on the next step up.

Moreover, unlike almost all presidents since the 1910 revolution who had come from the bottom, from lower-middle-class, mixed-blood families, the Lopez Portillos and on his mother's side, the Pacheco y Villa Gordoa family, had pedigree. They were white, of Spanish descent, not landed gentry but well-educated upper-middle class from that bastion of propriety and conservatism, Guadalajara. His grandfather had lived there as state governor of Jalisco, and so had his father, a civil engineer and oil executive turned historian.

Except for a short law course in Santiago, Lopez Portillo traveled little. He got his law degree at Mexico City's state university and opened his private law practice not far from there. After almost two decades as a prospering private attorney and law professor he told a friend he felt he was doing very much for very few people and decided to change the equation by turning to politics in 1962. Within a few years he was appointed to several high-ranking planning jobs at the Ministry of Natural Resources. Eventually, Echeverria made him finance minister in 1973.

So he seemed disconcerting, this rare breed of Mexican official, a man who suddenly decided to become a public servant at age 42 and with the help of friends and associates, had rapidly risen through the ranks. He had no large coterie of followers as did most high-ranking Mexican politicians, and he said shaking things such as "corruption is the cancer of this country" and "Mexico is not underdeveloped, it is underadministrated." His friends called him a "renaissance man" who painted, liked fencing and boxing and American football, and had published four books: two on constitutional law and two novels dealing with the mysteries of the Hispanic and the Indian. Mexico's blend of two strong cultures, religions andphilosophies. He speaks only a little English and French.

Mexico's more populist breed of politicians began to call him arrogant, elitist and impatient because he appeared less interested in flattery, demagoguery and symbolic speechmaking, which Mexico's politics thrive on. "He confuses people because he is straightforward," said an old friend of the new president. Other associates say he is not arrogant, but simply more candid, more independent and self-confident than most. The Punctual Pedagogue

Lopez Portillo naturally plays the role of the teacher. At news conferences he usually avoids the quick, glib political line and prefers to turn his replies into lucid mini-lectures, expounding on the whys and wherefores and developing alternatives on how to cope. Like the professor berating inattentive students, he may well start his answer by saying, "As I have said many times."

His meticulousness is apparent in his daily routine. He gets up before 7, jogs, does push-ups, swims, throws the javelin. He says he reads quickly through the five largest dailies "to see for myself how and where the stories are played" and reads extracts only of the foreign press.

By 8:30, well before the rest of the vast bureaucracy, he has started his day in offices at his residence. Lopez Portillo has practically given up going to the 17th-century presidential palace on that grand Spanish plaza known as the Zocalo.

His caravan, he realized, tied up Mexico City's already suffocating traffic even further. "He got embarrassed by the honking of the furious motorists," explained an aide. This shows a trait that manifests itself in other ways, an intellectual's bashfulness about the public exercise of power and the adulation displayed over a Mexican president.

When he gets long rounds of applause at public ceremonies, he will join the applause as though to confuse the issue, and when cheerleaders chant his name, he joins in the chorus, turning it into a joke.

Inevitably, admirers ask him to sign his two novels, but he likes to quip: "My success as an author is much improved since I got this job."

It took the people around him a while to get used to his punctuality, which seemed obsessive to a nation that prefers a sense of timelessness. "He gets infuriated when people keep him waiting," said a Cabinet member, "and he himself is more punctual than any Englishman."

Fiercely loyal, he has brought many of his old friends and associates into top positions and is very demanding of them. Several of his ministers are even childhood friends. He appointed his family doctor, Mario Calles, as minister of health while another close friend, Rosa Luz Alegria, became the first Mexican woman to join the Cabinet when he appointed her minister of tourism. Family Man

Now the consensus is that Lopez Portillo is one of the most liked presidents Mexico has had in two decades. Yet despite the fact that patronage is part of Mexico, the president has been strongly criticized for giving top jobs to many of his relatives, including his sister and his son.

He is known to be deeply sensitive about criticism of his family as he is about reports concerning his wife Carmen's frequent travels and propensity to spend.

This very public man is extremely private about himself and fiercely protective of his family. He sees his mother, who lives in the residence compound, every day, and is deeply attached to his three grown children, whom he talks about in sentimental detail. His son, Jose Ramon, he calls "my son-friend." When his elder daughter had her first baby he said it was "an extraordinary emotion to see my Gigi, my little girl, turned into a mother herself." He discovered "a marvelous new kind of love for that snotty pair," his two small grandchildren.

Last month at the wedding of his younger daughter, Lopez Portillo was visibly moved. "I came into office with three children and I am leaving [at the end of his term on Dec. 1, 1982] with none," he said woefully.

Although he is known as a warm, outgoing man with impulses of great generosity -- "one day he suddenly donated his private car to his driver," recalled a friend -- his close friends say they know little of his innermost thoughts.

Some of the boys of the Mexico City neighborhood, the Colonia del Valle where he grew up, remember "Pepe" as tough and ready to take on the bigger boys to defend the little ones.

One of those boys on the block is Mario Calles, the current health minister, who recalled, "Pepe seemed like one of us but then suddenly he'd disappear for two or three days. You'd think he was off on a binge. But no, he would go and sleep in the mountains. He liked to watch the stars and to meditate. He's always been a bit of a mystic and philospher."

But the thoughtful teen-ager could also have strong, down-to-earth reactions, recalled Calles. "He had three very pretty sisters who he was so protective of we didn't even dare ask them out. We were sort of afraid of Pepe, he was such a good fighter," Calles laughed. Policy & Patriotism

For all his criticism of the U.S., Lopez Portillo is not as passionately anti-American as many Mexican intellectuals. Yet, as a friend describes it, "he is deeply suspicious of the U.S. and its power designs."

Contrary to perceptions in the U.S., Lopez Portillo's approach to foreign policy is not ideological. It seems to stem from his strong sense of patriotism, his intellectual's belief in tolerance and his lawyer's respect for institutions and negotiation.

He criticizes both superpowers for their use of raw power and the U.S. in particular for turning El Salvador and all of Central America "into a political frontier of hegemony."

"An ideological position can be debated," he told the press here, "but a position of force if you are weak, never. We want the alternative of rationality instead of the fatality of hegemony."

He has reacted almost with a vengeance to what he sees as shortsighted and dangerous American policy in Central America. When Washington cut its aid to Nicaragua, he increased Mexico's aid to Sandinistas, to whom he feels an almost paternalistic attachment. In April, he received Daniel Ortega, coordinator of the junta as a hero in Mexico.

On many occasions he has said it is vital to help Nicaragua because it may be a new model, a "new starting point" for all of Latin America. He hopes the Nicaraguan revolution may produce the social justice Mexico's revolution lacked and the freedom that was sacrificed in Cuba.

According to aides, he has a very strong personal -- though not ideological -- rapport with Fidel Castro because he admires Castro's fighting spirit, his historical vision and his intellect.

Cuba's absence of freedom shocked Lopez Portillo, the liberal intellectual who is committed to freedom of thought. But when Washington recently stepped up its anti-Cuban offensive, Lopez Portillo reported publicly, "Cuba is the country most dear to us in Latin America."

Asked about his growing differences with Washington's view of the region, Lopez Portillo replied, "We are not an arrogant people out to defy the decisions of the powerful but a people with principles who have themselves felt what may happen to others." Mexico's close relations with Cuba, he said, "are designed to take advantage of our potential rather than being self-destructive with sterile conflict that stems from an artifical frontier between the superpowers." Life After Office

What will Lopez Portillo do after he hands over the presidency? He will name his successor sometime this fall who will then be endorsed by national elections.

"He will cultivate his love for horses," says an aide. Lopez Portillo rides and jumps whenever he has time and he endlessly doodles and sketches horses during work sessions. King Juan Carlos of Spain gave him a stallion and Lopez Portillo last January gave one to Ronald Reagan.

"Not so," says a lifelong friend of the president. "He will agonize over everything he could not achieve."

The answer of Lopez Portillo himself: "I will read, write and grow a beard."