Angry demonstrators confronted Miami's mayor today with shouted demands that he fire the police chief on grounds of racism and prosecute a Hispanic officer whose shooting of a black youth set off street violence last month.

The special city commission meeting marked the most dramatic moment so far in a month-long debate over how to prevent recurrence of the two days of racial unrest in Overtown, an area a few blocks from downtown.

The meeting followed a six-mile protest march by about 150 demonstrators that began at a video arcade where the violence occurred Dec. 28, and ended at City Hall on the lip of a placid yacht harbor bathed in winter sun.

The protesters provided Miami and its leaders with a reminder that, despite civic euphoria over the Super Bowl, the Overtown disturbances remain a bitter memory in the dilapidated neighborhood where they broke out, and that residents there single out Miami police tactics as the main reason for the violence.

"What do we want? " the marchers chanted. "Justice, justice."

Ray Fauntroy, local leader of the Southern Christian Leadership Conference, asked Mayor Maurice Ferre for action on demands that Police Chief Kenneth Harms, who is white, be fired and that Officer Luis Alvarez be indicted for shooting Nevell Johnson Jr., a 20-year-old black whose death touched off the violence.

His demand was backed by a dozen other black speakers who accused the city government of tolerating brutality against blacks and covering up for police crimes.

"If the officer is not tried and convicted, there will be more trouble," said David L. Perkins of the Community Advisory Committee. "If it an indictment of Alvarez don't come down, there's going to be more war. I know that."

City manager Howard Gary, who is black, reminded the shouting protesters that the state attorney alone has authority to determine whether Alvarez should be indicted. The city has conducted an investigation, he said, and State Attorney Janet Reno has promised a decision within two weeks.

"There has been no whitewash," Gary said. "There will be no whitewash."

Gary said he has "chastised" Chief Harms for referring to "hoodlums" during the unrest. But he reaffirmed earlier refusals to fire him. Ferre criticized Harms' "serious" problems with sensitivity to black feelings but contended the city charter makes Gary the only official empowered to fire him.

Ferre has named a blue-ribbon committee to study broader causes for the disturbances. He acted despite a sharp announcement from the U.S. Civil Rights Commission in Washington that it already studied and identified the causes and vainly called for action on them following similar unrest in Liberty City in 1980.

But most local debate--recalling that the police killing of a Miami black also contributed to the 1980 riots--has centered on police conduct before and during the disturbances and on overall police dealings with the Miami area's 17-percent black minority.

The questions have been complicated by Miami's large Latin population, which has tended to eclipse black concerns over the last two decades. Both policemen on the team that shot Johnson were Hispanics and, witnesses said, were speaking Spanish when the killing occurred.

Today, the two Hispanic members of the four-man city commission were absent from the special meeting, as was Harms.

Fauntroy and William Perry, president of the Miami Operation PUSH (People United to Save Humanity), have repeatedly called for Harms' resignation, charging him with ignoring "the pervasive prevalence of insensitive and inferior officers in his department."

Ferre, while praising Harms on some questions, wrote a memo to the city commission earlier this month also accusing the chief of doing too little to increase the department's "sensitivity to minority and human issues."

When Ferre's criticisms became public, Harms responded testily, saying he pleads "not guilty to the issue of insensitivity" and adding: "The community is going through a lot of aggravation. We don't need to be abused."

The Overtown violence broke out minutes after Alvarez shot and killed Johnson. Before it was over two days later, another black youth had been shot eight times and killed by police, allegedly for looting, and about 45 people, mostly young Overtown blacks, had been arrested in connection with the disturbances.

Police said Alvarez and his partner, Luis Cruz, had seen a gun in Johnson's belt and were seeking to disarm him. First indications were, police spokesmen said, that Alvarez' service revolver was fired accidentally.

The spokesmen also said Alvarez told of seeing a sudden movement by Johnson, as if he were trying to draw the gun police said was in his belt under a jacket.

By the time the street violence subsided, it had become known that Alvarez and Cruz were outside their assigned patrol area during the arcade visit. Harms described this as a violation of police procedure.

At the time, police spokesmen said that Alvarez, with 1 1/2 years on the force and seven citizen complaints in his file, was showing Cruz, in his first week on the job, how to work in a black neighborhood.

Since then, Alvarez, citing advice of his lawyer, has refused to testify to investigators on how he fired the fatal shot. He has been relieved of duty, with pay, pending the outcome of the investigation. Cruz had remained on the job until two weeks ago, when he also was relieved of duty after a superior discovered him secretly recording their conversation with a device hidden under his uniform.

While violence was racking Overtown, Ferre publicly questioned why Harms has not made more of an effort to assign at least one black patrolman to two-man squad cars in Overtown. Harms and other police officers resisted the idea, but the department announced today--just before the protest march--that three mixed patrols and some horse-mounted black officers will deploy in Overtown within two weeks.