In another political move paving the way for democratic parliamentary elections this spring, the Spanish government has decreed the dismantling of the monolithic state party founded by the late dictator Francisco Franco to preserve his authoritarian rightist regime.

The royal decree breaking up the 30-year-old National Movement, announced by the Cabinet late last night, was acclaimed by the opposition, which had demanded the dissolution of the Movement because its local chiefs throughout the country had the power to influence elections. More than 9,000 mayors representing the Movement are affected.

But Premier Adolfo Suarez is still left with the delicate problem of deciding on the legalizating of the outlawed Communist Party. The Supreme Court's fourth chamber officially confirmed this morning that it had disqualified itself from ruling on the party's legality and sent the controversial case back to the government. The government last month refused to recognize the Communists, proscribed by Franco during the 1936-39 civil war, and asked the court to make a final decision.

The Communist Party's executive committee met here today at its headquarters to study the setback and plan strategy. A statement after the session warned that if the party is not "legalized, elections are threatened." The statement remarked that the court's decision has "opened a grave political crisis."

The Communists called on all opposition parties to press the government for legalization and indicated that they will ask the opposition to abstain from the election if the party fails to obtain legal standing. The voting will be the first free parliamentary poll in Spain in 49 years.

Many members of the opposition - and some government officials - feel that the monarchy's plans for a democratic Spain could falter if the Communists are not allowed to take part in the election. The party has the power to call strikes that could cripple the depressed Spanish economy. Even though the party remains illegal, it has been operating openly for months and the government tolerance had given the impression that legalization was imminent.

While the Communist issue clouded the political scene, there was no immediate reaction from the rightist National Movement's leaders. The movement is firmly under government control. Its secretary, who has Cabinet rank, is a close political collaborator of the premier. He has been paving the ground for breaking up the powerful organization Franco called his "cheering section."

For many Spaniards the breakup of the movement means the end of the Franco era. "It was his creation," said a government official. "He considered it was the framework of his new state and believed firmly that it would last forever."

Still in the constitution, however, are the principles of the Movement. All officials had to swear allegiance to the Movement and its "immutable ideology on taking office. When Juan Carlos was sworn in as king following Franco's death, he had to take an oath pledging to uphold the movement and its political philosophy.

Under the terms of last night's decree, many of its functions will be transferred to existing ministries. The Movement's 35 newspapers and 44 radio stations will be taken over by the Information Ministry and become part of the state-owned media network. The Movement's extensive bureaucracy will be absorbed by the government. Its vast assets, which include property owned by Republican organizations before the Civil War, will be transferred to the finance Ministry.

The Movement was a coalition of the rightist forces that supported Franco during his successful three-year uprising against the Second Republic. Its top body was the National Council, an ideological watchdog with little power. But Franco used it for ceremonial purposes at sessions attended by members who wore the Movement's uniform - Blue shirt and white blazer, derived from the Falange, the country's fascist party.

Opposition to the Communists was strongest among the Movement's membership. Its downfall marks the removal of a major Farnco institution patterned on Nazi German and Italian Fascist World War II models.