Mexican President Jose Lopez Portillo received gifts of California wine and a rifle from President-elect Ronald Reagan's personal collection today as the two men attempted to initiate a personal rapport that they hope will help them address problems between the United States and Mexico dating back generations.

Although outwardly, all was warmth and cordiality between the two leaders, substantive issues were mostly left for a later date, according to people who attended the meeting.

Mexican presidents have been meeting with their counterparts from the United States since Porfirio Diaz and William Howard Taft got together here in Ciudad Juarez in 1909, and they always talked about being good neighbors and attempted to sidestep the common feeling among Mexicans that they were really regarded as poor and very distant relations.

Mexico, however, is not the same neighbor today as it was 70 or even seven years ago. It is a country full of new-found wealth and new ambitions and, as always -- but with a good deal more clout these days -- a fierce sense of its own independence.

Although its leaders refrain from calling Mexico a "power," its size, its population, its location and now its oil have made it just that in the region -- a new major power, at least in local terms, capable of challenging and in some cases already competing directly with the United States.

Mexico, as Lopez Portillo said last September, expects to have "a worthy place standing erect in the world and not a seat in a sphere of influence."

Mexicans are generally optimistic about resolving what have been some of the toughest bilateral issues with the United States, but they see others emerging rapidly that could cause serious problems.

They expect, for instance, that over the long run a conservative administration in the United States will be more receptive to the millions of illegal Mexican workers there than one with strong labor ties, although there are concerns about protection of the illegial immigrants' rights.

Even on the difficult question of oil, as long as the Reagan administration does not try to exert pressure for more production and more exportation the Mexico's leadership feels it wants to or can handle, friction should be slight.

Nevertheless, there are fears here what many Mexicans see as a new American drive to reassert, as Secretary of State-designate Alexander Haig put it, "a firm, unambiguous demonstration of renewed U.S. strength and ability to lead."

Mexicans worry constantly that Washington will somehow try to return to the days of "the big stick" in its policy toward Latin America, and part of the purpose of the meeting today was to seek reassurance that this will not be the case and that Mexico will be consulted -- and its views taken into account -- before the United States makes any major moves in this country's own growing sphere of influence.

As Mexico expands its interests, Mexicans know from experience, they inevitably collide with those of Washington.

Fishing provides one example. For Mexico, a burgeoning major fishing power, tuna fishing rights have become a sore point between the two countries, and on Dec. 29, Mexico unilaterally abrogated all its fishing treaties with the United States after 15 meetings since 1977 failed to straighten out the issue.

On foreign relations, Mexico generally is more tolerant of the leftist movements in the region, attempting to maintain cordial ties with them even at the expense of good relations with what the Mexican press regularly refers to as repressive or even "genocidal" governments in Guatemala and El Salvador.

One Reagan adviser privately refers to this as Mexico's "surfing on the wave of the future," which the Mexicans believe is coming from the left.

In the case of Nicaragua, to which several Reagan advisers have said they would like to cut off aid, Mexico has adopted a fraternal relationship with the Sandinista leaders who are so suspect in the new Washington. The Mexicans worry that the Reagan administration will intervene in the area to stop possible Marxist takeovers.

Mexican Foreign Secretary Jorge Castaneda said in December that he had no way of knowing what Reagan's policy would be, but obliquely cautioned that "it could trigger difficulties between the U.S. and Mexico in the region. We shall maintain Mexico's traditional position, which is nonintervention in the internal affairs of other nations or the right of people to choose the government they wish."