King Juan Carlos today inaugurated the new Spanish parliament with an explicit endorsement of the democratic process that swept the Socialist Party to power in national elections a month ago.

The 44-year-old monarch told congressmen and senators assembled in the ornate Congress of Deputies debating chamber that there was reason for satisfaction at the "orderly, peaceful and free manner" in which the Spanish people had expressed their will in the voting. Flanked by Queen Sofia and Crown Prince Felipe, Juan Carlos said: "Political changeovers, decided by the people, are normal events that form the essence of democracy."

The Socialist Party, led by Felipe Gonzalez, won outright majorities in the Congress and Senate in the Oct. 28 elections. Gonzalez will take office next week at the head of the first left-wing administration in Spain since Francisco Franco and the Army overturned the republic in the 1936-39 civil war.

The ceremony contained deep symbolism, marking a formal reconciliation between the country's left wing and the monarchy. Fifty years ago Juan Carlos' grandfather King Alfonso XIII chose exile when the left triumphed in elections and proclaimed a republic.

In what was seen as the definitive burial of the Socialist Party's past conflicts with the monarchy, the new Socialist speaker of the house, law professor Gregorio Peces-Barba, warmly welcomed the royal family, saying the parliamentary monarchy, represented by Juan Carlos, ensured "stability, equilibrium and the possibility of progress."

Juan Carlos, once viewed as the figurehead successor to the dictatorship of Franco, who groomed him for power, earned the profound respect of the left for his determined sponsorship of the post-Franco transition to democracy. When the king almost singlehandedly quashed an attempted rightist military coup two years ago he became the most admired figure in the nation.

The king's endorsement of the Socialist victory was coupled with an appeal for caution. He told the new legislature that "this is the time to practice . . . prudence, the supreme virtue in politics. Without it the laws we need would not be possible, and I ask you to apply it unstintingly in this new parliament that opens at a crucial moment in our history."

There is an undercurrent of fear in political circles here that should the Socialists fare badly in power, rightists would be tempted once more to seek out the support of the military as at the time of Franco's rebellion. The ruling Center Party was routed in the vote, and the conservative Popular Alliance party headed by Manuel Fraga, a former minister in the Franco government, emerged as the main opposition party.

In a reference to possible conspiracies, Juan Carlos said pointedly: "The wishes of a minority, supported by force, can never prevail over the freely and peacefully expressed will of the majority."

Highlighting the continuing crucial status of the armed forces in Spain, the king singled the military out for special tribute as the main victims of political terrorism and as "the firm and worthy guardians of the state of law." Juan Carlos, who wore the ceremonial dark blue uniform of a field marshal, stated his "respect, admiration and gratitude" to the armed forces.

Prior to his inauguration, Prime Minister-elect Gonzalez has kept a low profile, avoiding the media and holding long working sessions with his closest aides and with the outgoing centrist administration. There are indications that the 40-year-old Socialist leader is following the royal counsel of prudence and has chosen a moderate government team.

Socialist sources said chief economic minister in the new government would be an experienced administration official, Miguel Boyer, who has close ties to banking and business interests and stands politically on the right in the Socialist Party.

The key post of defense minister reportedly has been assigned to the Socialist mayor of Barcelona, Narcis Serra, a party moderate. The sources said the new foreign minister would be a career diplomat, Fernando Moran, who has held senior posts in the ministry.