Attorney General Benjamin R. Civiletti launched a sweeping federal investigation of old and new complaints of police brutality today as this city of palm trees and gleaming boulevards slowly and cautiously began recovering from a three-day nightmare of bloodshed and arson.

Civiletti, dispatched by President Carter to help calm the nation's worst race riot in more than a decade, warned that while the trouble here "is partially quelled, it is still seething. We can't expect to return to normal without action" to address what blacks here see as "two separate and unequal standards of justice."

Civiletti announced that he is sending up to three dozen additional federal prosecutors, U.S. marshals and FBI agents to investigate not only last week's acquittal of four white ex-policemen in the killing of a black insurance salesman, but "all serious allegations involving violations of civil rights and brutality" in Dade County.

A federal grand jury is to convene Wednesday to hear evidence on the death of black insurance man Arthur McDuffie, the case that touched off the riots. Grand jury summons were issued today to several Dade County policemen to testify next month.

While more than 7,000 peace officers kept guard over the burned-out, 18-square-mile black community of Liberty City, the other Miami seemed to relax visibly. Rolls Royces returned to Biscayne Boulevard. Tourists toted folding chairs to the sands at Miami Beach across the causeways.

A few fires burned on today in the modest store fronts along 22nd and 27th Avenues, but no deaths or injuries were reported since a black man was gunned down by police Monday evening -- the 15th fatality since the riots started Saturday night.

Almost 52 square miles of the city were under curfew tonight. Liquor and gun sales remained forbidden. Schools were to stay closed again Wednesday, and gasoline sales were restricted to the tanks of motor vehicles.

In the heat of the midday sun, a few white merchants ventured out to survey their looted stores.

"I started this business 16 years ago in my garage," said S. S. (Joe) Skiddell, surveying the blackened remains of a small, squat warehouse from which he sold home bartending equipment.

"Now there's nothing left. I never had insurance -- it was too hard to get in this neighborhood. Now I've lost $100,000 worth of merchandise. I'm going out of business for good."

Thirty years ago, Skiddell, now 76, retired from Chicago to Miami Beach, where thousands of elderly whites dwell in air-conditioned condominiums and nicely landscaped homes, far from the poverty and frustration of Liberty City.

His bitterness attests to the fact that racial animosity here is a two-way street. "Whites are being pushed around by blacks," he said. "The governor should have issued orders to shoot. If he had done that, we wouldn't have had all this burning. The only way to stop violence is with violence -- especially when they become savages."

A few blocks away from Skiddell's warehouse, "Uncle Arthur's" grocery store sits untouched on a corner, its shelves piled high with canned goods, its racks full of pantyhose. Proprietor Arthur Brooks, 55, spent three nights in the store, when rioters and looters saw he was black, they left him alone.

Since the white-owned grocery stores in Northwest Miami were gutted over the weekend, Brooks says he is selling 20 percent more merchandise. "But it doesn't make me feel good at all," he said. "I don't enjoy reaping this kind of benefit. This is a very unfortunate situation."

Most stores in the riot area were burned and looted. Officials estimated that the damage had put 2,500 people out of work.

By early this afternoon, the streets had come to life in Liberty City. Barricades had been lifted, firebombed cars had been towed and traffic resumed. Helmeted National Guardsmen carrying M16 rifles were visible every few blocks, but they seemed relaxed, lounging and chatting with black residents.

Bus service was phased back in. Fire trucks, which earlier had refused to enter the riot corridor, were trying to dampen simmering flames along 27th Avenue.

Utility company crews, which had stayed clear of the area because of snipers, moved in to restore power to 3,000 homes and businesses.

But in the parking lot of a looted Grand Union store, surrounded by the stink of rotting food, Joseph Leroy Smith, a 39-year-old laborer, took no comfort in the return to quiet. "Look at my car," he said.

The windows of his 1972 Chevrolet Impala were smashed with the shattered glass strewn over the car seat. The word "looter" was spray-painted on the trunk.

Miami police said the city would "assume responsibility" for the vandalism of more than a dozen cars left overnight Monday in the supermarket parking lot. Black residents said police slashed the tires and spray-painted the cars.

Police said today 936 persons had been arrested since the rioting began, of whom 818 were black and 118 were white. Most were released from custody.

City officials feared that the violence would affect tourism just as Miami is gearing up to receive what was expected to be its largest number of foreign visitors ever. One large convention cancelled at the Omni Hotel.

In the lobby of the 37-room Sunset Motel in Miami Beach, owner Adele Burstyn, 52, sat watching a TV soap opera. "Normally I have 80 percent occupancy," she said. "Now I have half that. People are not coming down. They don't want to get involved in this mess."

Burstyn said her maid has been too scared to leave her house, so none of the motel rooms has been cleaned in three days. "It's very dangerous here I just stay locked up at home," Burstyn said.

While blacks make up slightly more than 15 percent of the Miami area's 1.6 million residents, 13 percent of the city police, and 6 percent of the county police, are black.

In Tampa, meanwhile, police sealed off a black neighborhood on the city's east side for the second straight night tonight following reports of rock-throwing by roaming mobs.

At least one fire and several minor injuries from flying glass were reported, but police Capt. Johnny Perkins said the incidents were "nothing disastrous." He said a "relatively large" number of black youths were involved.

The incidents took place in that same area where disturbance were reported Monday night. Earlier, police had said the streets were quiet after morning incidents in which blacks pelted cars with bricks and bottles.

At the University of South Florida campus, several buildings were painted with civil rights slogans, according to United Press International. Police said at least three groups of juveniles were involved in rock and bottle throwing late Monday night and early today. A liquor store, a meat market and a grocery store were looted, and windows at a dry cleaners were broken.

An 18-year-old white youth was beaten by several blacks when his car broke down. He managed to escape, and returned a short time later with a friend. When a large group of blacks started after them they fled. His car was overturned and its windows shattered.

Two other persons in another car were cut by glass from a shattered windshield, and a police officer suffered minor injuries when he was struck in the eyes by flying glass.