Dissatisfaction with President Efrain Rios Montt of Guatemala has risen to the highest and most volatile level in 15 months of his rule, opening the prospect of new problems for the United States in troubled Central America.

Rios Montt, 56, a retired brigadier general who says God called him to office, appears to have weathered the latest of more than a dozen serious challenges to his leadership for the time being, according to Guatemalan and diplomatic sources.

But his hold on power was shaken last week when he declared a "state of alarm" following rumors of an attempted coup. Unless he accommodates Army officers restless under his command, they say, the outcome could be another coup like the one that brought him to power March 23, 1982.

In addition to general interest in stability and return to constitutional government in Guatemala, the Reagan administration has expressed support for Rios Montt personally. According to knowledgeable sources here, it would view his removal by fellow officers as a setback for efforts to deal with the crisis in Central America.

Rios Montt has mounted a relentless and often ruthless campaign against leftist guerrillas in the Guatemalan highlands that has seriously weakened rebel strength. For an administration that has defined such guerrilla threats as a challenge to vital U.S. interests--and is having difficulty meeting a similar threat in neighboring El Salvador--such relative success has made Rios Montt look good.

In addition, a takeover by other military officers would create a new unknown in the already complicated Central American picture. Under Rios Montt, the most populous Central American country has been helpful to Washington in diplomatic confrontations over leftist-ruled Nicaragua and has improved a benighted human rights situation that had led to a five-year cutoff of U.S. military aid.

Within Guatemala, however, resentment has been building steadily in recent months over Rios Montt's style of government, which has led some Guatemalans to describe him as the Central American "ayatollah." This is a reference to his authoritarian rule as well as his frequent invocation of divine inspiration.

"He feels he has a messianic mission," said Vinicio Cerezo, leader of the Christian Democratic Party.

Rios Montt, a former Roman Catholic, is now an elder of the Christian Church of the Word, an evangelical Protestant sect. Two other elders, Francisco Bianchi and Alvaro Contreras, are close personal aides with nearby offices and daily consultations. As part of the mix between religious and political duties, Rios Montt gives frequent Sunday night sermons over Army radio and television, preaching the fundamentalist morality that he has made the underpinning of his government.

In this predominantly Roman Catholic country, the church hierarchy increasingly is chafing under what clerics see as use of state power to further Rios Montt's brand of religion at the expense of Catholicism.

The tension grew significantly in March when Rios Montt rejected church entreaties and allowed the executions of six men condemned by closed tribunals only four days before the arrival of Pope John Paul II during his Central American tour. In reaction, the Roman Catholic Bishops Conference issued a pastoral letter six weeks ago criticizing "abuse of power," the closed military tribunals and reported massacres of Indians suspected of aiding leftist guerrillas.

Criticism also has grown sharply among businessmen, mostly over government plans to impose a value-added tax for the first time in Guatemala. The tax not only would take more money from a business class accustomed to low rates. It also would reduce widespread tax evasion by providing government inspectors with a tracking system.

The new tax is part of economic reforms imposed by the World Bank as conditions for a $120 million balance of payments credit, sought by Guatemala to help meet $400 million in hard currency debt. Previously due to go into effect July 1, it has been postponed until next month because of strong opposition.

Some wealthy businessmen were so upset at the prospect of such a tax that even before last week's crisis they were feeling out Army officers with offers to finance a coup to get rid of Rios Montt, according to reports circulating among diplomats here.

Aside from the projected tax, businessmen and others are feeling the brunt of an economic decline that has struck across Central America because of low prices for such key exports as coffee and fallout from recession in the United States. Exports declined 30 percent last year, for example, and are likely to drop again this year.

"It is not by any means the worst economic situation in the world, not even in Central America, but it has made the problems of the government in power that much more acute," a diplomat said. "And that happens to be the government of Rios Montt."

Against that already contentious background, political parties recently intensified calls for early elections and a return to constitutional rule as pledged by Rios Montt when he was installed in power by a group of young officers.

Rios Montt has been promising to hold elections for a constituent assembly with undetermined powers in the second half of next year. Late Wednesday, bowing to pressure from dissatisfied Army officers, he had his government set July 29, 1984 for those elections and Sept. 15, 1984 for the assembly's first day of work.

Guatemalan politicians quickly pointed out that Rios Montt still has not set a date for presidential elections and that the constituent assembly has not been guaranteed power to do so even after it sits. Moreover, the timetable envisaged by Rios Montt--assembly next year, elections in 1985 and a turnover of power in 1986--falls far short of demands from Guatemala's main political parties.

Rafael Escobar Arguello, a spokesman for Rios Montt, said the delay is necessary to give new parties time to organize, particularly left-leaning groups that previously were banned and found expression only in guerrilla warfare. Traditional parties, rightist and centrist, are urging swift elections to gain advantage over potential adversaries from the left, he asserted.

"We had 12 years with four fraudulent elections," said a shopkeeper who agreed. "In 15 months it is impossible to build a system that will not be fraudulent. They should be more patient."

Political leaders fear, however, that in fact the delay betrays a conviction by Rios Montt that only he can right the country's wrongs and that, when the time comes, he will find another reason to delay the elections indefinitely.

"He has the stuff to become a real Pinochet," said Alejandro Maldonado of the centrist National Renovation Party. "That is, he thinks he has a vision, a mission for which four years are ridiculously short."

Gen. Augusto Pinochet took power in Chile 10 years ago, he recalled, with a promise for swift elections and constitutional rule.

In early June, the various sources of opposition to Rios Montt appeared to be coming together in a concerted campaign. Jose Guillermo Echeverria Vielman, a reserve brigadier general, published a letter criticizing Rios Montt for mixing religion and politics, abusing power and contaminating the Army by associating it too closely with his government.

Political and Roman Catholic leaders quickly seized on the letter and added their own criticisms. They were able to do so publicly because Rios Montt had lifted Guatemala's state of siege restrictions last March to mark the first anniversary of the coup. By last week a number of Army officers were meeting with Rios Montt demanding a change in style and substance to end the dissent, they added.

As a background to their discussions, Guatemalan political sources said, several officers were threatening to lead their troops into armed revolt from bases in the countryside.

The officers, particularly younger commanders who played key roles in putting Rios Montt into power, were especially upset over allegations that six officers seconded as advisers in the national palace were taking bribes and disrupting the military chain of command by handing out orders to superior officers outside the palace.

As the officers confronted Rios Montt with what reliable sources said was a demand for his resignation, two political opponents broadcast resignation appeals over television Tuesday night. Palace officials understood this as a concerted maneuver designed to precipitate a coup, the sources said.

By Wednesday morning, Rios Montt was holding secret meetings with the military leadership behind a reinforced guard at the national palace. After a tense day, he announced a "state of alarm" and fired the six young military aides. Later that night, he had the assembly election dates announced, apparently responding to the officers' demands.

Political sources said more changes also were discussed, including possible removal of presidential aides connected to the Church of the Word. Escobar said a "reorganization" was under way and cited as the first example removal of 50 officers from ministerial posts. To go along with the concessions, however, an armored vehicle with a cannon mounted on the top was posted at the main entrance to the national palace, pointing toward the city's central square.