Antonio Ramalho Eanes, Portugal's soldier-president, likes to go horseback riding in the capital's Monsanto park on Sundays. But the last thing he wants to be is a man on horseback.

The chaotic course of Portuguese politics, however, has forced him to risk having the politicans accuse him of just a temptation.

Eanes, in his first interview as president, made clear that he does not believe his small country, beset with major economic problems, can afford a democracy whose politicians believe in politics as usual.

"There has been os much ideology in this country that people are fed up . . . The people are not seeking political brand names but achievements," he said.

The stern Eanes, 43, was a gymteacher in the army. He grips the wooden arms of his chair in Belem Palace as he were afraid he might start gesticulating. But unlike in his public appearance, he offers a shy, almost relaxed smile occasionally.

Eanes indicated that althoug he is offering the politicans in parliament a last chance to get together on a government, he is not going to wait very long. "I'm disposed to give them the time they ask for - if the political situation allows it."

In a solemn address to the nation Friday night following a week of self imposed silence, Eanes refrained from setting any time limits. But in the interview he said tha tif they have not shown within a week that they can form a coalition, he will move into the next phase - an attempt to form a government headed by an independent figure with party mea under him in the Cabinet.

That approach, Eanes said, would get another week's try. If that failed, he would appoint a Cabinet for the sole purpose of preparing new elections. The present political leadership is parliament, especially the Socialist Party of former premier Marie Soares, can expect ot emerge greatly diminished in such a contest.

His approach to politics is novel in a country given to expansiveness, position-taking and overstatement. Eanes said he had refused to see any politicans in the week's interval between the fall of the latest government and the presidential address to the nation because "everybody needed to reflect calmly, to de-dratatize things and to have a little silence for a few days."

The Socialist Party, in its first reaction to the speech yesterday, complained about this refused to talk things over. Most of the other parties, including the Communists, hailed the president's speech.

Eanes finally said he would start seeing the party leaders on Tuesday.

One of the leaders he is likely to have the most relaxed talk with is Communist party chief Alvaro Cunhal, although in 1975, Eanes led the military men who headed of a Communist takeover. Since having theif union demonstrations forced off the streets by Eanes' soldiers, the Communists have been on their best behaviour.

Speaking of the Communists, Eanes was free with his compliements. "Compared to other parties," he said, "the Communist Party does not have the same type of problems that leap to the eyes of the militants and the population. They project an image of capability, of cohesion and of organization that leaves a good impression, even to outside observers . . . The Communist Party doesn't try any more to impose its ideogoly but rather to offer solutions to problems. To solve those problems it sometimes uses the most competent people even if they don't belong to the party."

In contrast, Eanes' most tense talk is likely to be with the Socialist Soares. Although the president insists he could work smoothly with Soares again, Eanes showed in his speech that he has not yet forgiven his expremier for having "subjected the regime to excessive risks and dangers."

This summer, Soares outraged Eanes' military sense of honor by going back on a pledge to resign as premier if his party, the largest in parliament, lost the majority it enjoyed through a coalition.

When Soares told Eanes that his party wouod not let him resign after all, the incensed president dismissed him.

Eanes was once quoted by a Brazilian journalist in what was supposed to be an off-the-record conversation as saying he dislikes Soares personally. Some analysts hold that the two men are condemned to work with each other since recent events show that neither can rule wihtout the other. Eanes seems to be out to prove, however, that is not necessarily so.

THe threat of elections gives the president the upper hand, even though he says he would rather avoid them. The uncharismatic Eanes, who reads his TV addresses with his eyes glued to his text, seems to be at the height of a personal prestige, surprising the popularity he enjoyed when he was elected president with nearly 62 percent of the vote in 1976.

Now, Eanes seems to be working out a direct relationship with the electorate that reaches over the heads of the politicans. "Democracy," he said, "shouldn't be a game in Lisbon between the parties and the president, but something involving the whole population. Maybe that is too ambitious an approach. We shall see . . . It is my historical responsibility," he said, "first to consolidate democracy and second to act so that the consitution works fully to let the Portugues people see both its defects and its good points. Then the people could say what changes thay may possibly desire, including the kind oof presidency they want in the future."