A move by the Argentine military to grant political asylum to several leading members of Bolivia's recently overturned military government has strained Argentine relations with South American democracies and could touch off a dispute with U.S. justice authorities.

The Argentine Foreign Ministry announced last week that political asylum would be granted to Bolivian ex-interior minister Luis Arce Gomez, an Army colonel, who arrived in Argentina shortly before the new Bolivian democratic government of President Hernan Siles Zuazo took power Oct. 10. The Bolivian Army had ordered Arce Gomez to return.

Foreign Ministry officials, who asked not to be identified, also said Argentina would grant asylum if necessary to Gen. Luis Garcia Meza, the leader of the Bolivian military coup of July 1980 and president for 13 months.

Arce Gomez and Garcia Meza have been accused repeatedly by Bolivian authorities and foreign diplomats as the key leaders of one of the most corrupt and violent governments in Bolivia's turbulent history. Both have also been charged with direct involvement in Bolivia's booming cocaine traffic.

The new government in La Paz has launched a series of investigations into alleged illegal activities by the two, and Arce Gomez has publicly conceded that he was responsible for the organization of paramilitary squads involved in political murder.

Reports in the United States have said that Arce Gomez is under investigation by a grand jury in Miami looking into cocaine trafficking, and U.S. officials have said they may seek his extradition from Argentina.

The presence of the two Bolivians is an embarrassment for the Argentine government, which has pledged to return its own country to democracy by early 1984 and has sought to solidify strong Latin American support for its claim to the Falkland Islands.

But military leaders here, who supported the 1980 Bolivian coup, have strongly backed the refugee officers while sharply attacking the fragile new government in La Paz. Army officials have said they are worried by socialist Siles Zuazo's perceived leftist tilt.

Bolivian spokesmen have warned that Argentina may assist the exiled Bolivians to mount an attack on Siles Suazo's government--just as Argentine authorities backed the coup that annulled his election in 1980.

"One day the Argentine military dictatorship crossed the frontiers of my homeland to install another dictatorship," said Bolivian Senate Vice President Oscar Zamora Medinaceli on a recent trip to Buenos Aires. "The time will come when no dictator in America will be able to seek asylum in another American dictatorship."

In La Paz, Reuter reported today, the government announced that two men -- one of them an Argentine -- attacked Vice President Jaime Paz Zamora yesterday but he was not hurt. Paz Zamora is acting president while Siles Zuazo is away on a trip to New York.

Spokeswoman Marlene Berrios identified the alleged assailants as Carlos Fajardo and Argentine Mario Mignola. Both were arrested. She said the Argentine had been identified as a member of one of many illegal paramilitary groups set up while the military was in power.

Argentine officials have sought to limit the political damage of sheltering Bolivians by arguing that political asylum is a long Latin American tradition and by placing a series of conditions on Arce Gomez's stay. The strictures prohibit the flamboyant colonel from making statements about Bolivia or from living near the Bolivian border.

Foreign Ministry officials nevertheless concede that the Argentine military move has damaged Argentina's diplomatic position.

One government official, a civilian who asked not to be identified, said "it could cost us a long, slow, involved political battle. The problem is we can't just let Arce Gomez go. You know who his friends are."

The trouble over the Bolivians has come at a time when Argentina's international diplomatic position already appeared to be eroding, despite the recent passage of a U.N. resolution backing its call for negotiations with Britain on the Falklands.

In addition to protests from the Bolivians, Venezuelan President Luis Herrera Campins recently called off a planned visit to Argentina. Herrera, who only months ago emerged as Argentina's strongest ally in the conflict with Britain, reportedly said that he would not set a date for his trip until the Argentine military set a firm date for the promised democratic elections.

The pressure from Latin governments, also disturbed by reported Argentine military involvement in Central America, has been matched by renewed efforts by European governments to force action on cases of persons who "disappeared" during military rule.

In recent weeks, the governments of Italy, France, West Germany, Spain, Sweden and Switzerland have requested that the military clear up cases of disappearances by their nationals who presumably were killed during the military's campaign against internal opponents in the 1970s.

The combined effect of these protests, officials here concede, has been to weaken Argentina's chances of forcing Britain to negotiate its claims of sovereignty to the Falklands--a primary goal of Argentine foreign policy. "Despite the triumph in the U.N., Argentina remains alone," said a recent headline on the cover of the pro-government magazine Somos.

While Arce Gomez and Garcia Meza have received the most attention, they are not the only Bolivian military refugees believed to be in Argentina. Following the collapse of the military government in late September, at least three other high-ranking officers were widely reported to be in Argentina, including an ex-president, Gen. Celso Torrelio Villa, a military college director, Col. Fausto Rico Toro, and the former head of the Army special security services, Col. Freddy Quiroga.

It was Arce Gomez who caused the most trouble for Argentine officials. While the others remained in seclusion, he unexpectedly showed up at a press conference last month by the visiting Bolivian defense minister.

Arce Gomez denied to the surprised reporters that he had been involved in Bolivia's narcotics trade, but admitted that he had organized paramilitary squads to attack military opponents. In addition, he said, "I am the responsible one" in the celebrated political murder of Marcelo Quiroga Santa Cruz, a Bolivian Socialist leader.

In the following days, Arce Gomez continued to visit the offices of prominent Argentine newspapers for interviews, and posed for pictures displaying the long knife he kept strapped to his leg. He repeated his earlier confessions and added to one reporter, "If I had wanted to kill I would have killed Siles."

Officials have banned Arce Gomez from making further statements. His apartment in Buenos Aires remained vacant and the building's staff said he had moved from the capital. "There were too many reporters waiting around here," one member said.