ALGIERS, JUNE 13 -- The leader of Algeria's triumphant Islamic fundamentalists today renewed demands for the dissolution of parliament and new legislative elections as partial returns confirmed the fundamentalists' upset victory in municipal and regional contests.

But with shock waves still reverberating around the Arab and European shores of the Mediterranean, Abbassi Madani sought to reassure Algerians and the country's neighbors that his Islamic Salvation Front favors moderation rather than an intolerant brand of radical Islam.

Stunned officials of the government remained silent throughout the day as ordinary Algerians tried to come to grips with the implications of the end of a three-decade era during which the now decisively repudiated National Liberation Front (NLF) monopolized power.

So, too, did officials in France, the former colonial power here, and in neighboring Morocco and Tunisia, whose governments have been worried since Algeria last August became the first North African nation to legalize a fundamentalist party.

{French President Francois Mitterrand said he hoped France would continue to have good relations with its former colony, the Los Angeles Times reported. But privately, Mitterrand aides said they feared the results would exacerbate popular fears in France about the 4 million Moslems there.

{Jean-Marie Le Pen, leader of France's extreme right-wing National Front, told the Times that the fundamentalists' victory is likely to lead to more immigration. "If there is trouble in Algeria," he said, "many more will try to come here. The vast majority of French are opposed to any increase in immigration."}

Partial results released by Interior Minister Mohammed Salah Mohammedi showed the fundamentalists captured 327, or 53 percent of the 612 municipalities counted so far in Algeria's first multi-party elections since winning independence from France in 1962.

The NLF, which led the war of independence against France and has ruled ever since, captured 208 city halls, or 34 percent.

The Rally for Culture and Democracy, representing the Berber minority, won control of 54 municipalities, or 8 percent, with the remaining 5 percent distributed among independents and minor parties.

Speaking at an evening news conference, Mohammedi provided no breakdown of the popular vote, confirmed that an unusually high 40 percent of voters abstained and promised final results for all 1,541 municipalities by Thursday evening.

Hours earlier, Madani repeated fundamentalist campaign demands that the government resign and dissolve the parliament. He insisted that national-level elections should take place no later than 90 days after dissolution of parliament.

Madani suggested the question should be put to a referendum if President Chadli Bendjedid, whose term expires in early 1992, decides against dissolving parliament.

Madani said he did "not rule out a coalition" with any political group and sought to disarm critics who say the Islamic Salvation Front rejects cooperation with secular political parties. "We are going to guarantee freedom of all opinions," he said.

Madani, 59, a university professor, also rejected suggestions that the Algerian armed forces were hostile to his cause. Senior military officials had warned during the campaign that they would not tolerate attempts to subvert the country's nascent democracy.

Political scientists studying partial results said the high absentee rate assured the NLF's defeat. They noted heavy abstentions came not just in big cities, as had been widely predicted, but also in its once-solid rural heartland.

Throughout the country, these analysts said, many people decided to abstain rather than vote for either of the main parties.

This analysis tended to undercut suggestions that revolutionary war hero Hocine Ait Ahmed's call to boycott the elections, widely followed by members of his Berber minority, had by itself assured the fundamentalist victory.

But academics and analysts predicted that these normally minor elections could entirely rearrange the political landscape, especially if disparate lay forces that were virtually eliminated Tuesday by the two big parties prove capable of coalescing into a meaningful political force.

The president's entourage long has had hopes of splitting the NLF and forming a new party around him dedicated to carrying out ambitious economic reforms aimed at solving Algeria's serious economic problems. Bendjedid supporters said they take comfort in the disgrace of the NLF's old guard, which opposes the reforms and, they said, now bears responsibility for the unsuccessful election campaign.

Mohammed Yazid, a veteran revolutionary who heads an official think tank, consistently has warned that the NLF must reform itself or be consigned to political oblivion.