Swedish Prime Minister Olof Palme was shot with a .357 magnum bullet, of a copper-tipped type not seen here before, police said today.

Such details have led police to conclude that the killing was carefully planned, perhaps carried out by a professional. But they said they have made no arrests and have no suspects nor indications of a possible motive.

Meanwhile, the provisional Swedish government under Acting Prime Minister Ingvar Carlsson met this afternoon and confirmed that he would make no changes in Palme's Cabinet. His Social Democratic Labor Party, whose parliamentary majority is expected to confirm Carlsson in a March 11 vote, said Palme's funeral will be held March 15.

One of Palme's closest associates in the party, a top adviser on foreign affairs, said that a broad range of government and political leaders was expected to attend in tribute to Palme's record and reputation. As an indication of Palme's wide appeal and contacts, he said, Nicaraguan President "Daniel Ortega and Henry Kissinger both called me last night" to offer condolences.

Witnesses who saw the single assailant as he ran from the scene, including Palme's wife, Lisbeth, have said that he was dark-haired and wore a black, three-quarter length coat.

Police officials said Mrs. Palme, who was walking at her husband's side on a downtown Stockholm street when he was shot, "hadn't seen the man before." But, in one of a number of seemingly conflicting pieces of information here, another well-informed source close to the family said she had told investigators that she may have seen the man before, but did not know where or when.

Senior police officials firmly rejected speculation in some international media that the killing could have been connected to anyone known personally by Palme or his wife. "There is no known connection between the murderer and the victim," Stockholm police commissioner Hans Holmer said.

Nearly 1,000 persons have volunteered information or have been questioned in the investigation. The latter category includes members of exile and refugee groups that have come to police attention in the past, or whose countrymen have been involved in previous political violence here. Among them are Kurdish exiles, Croatian separatists and West German radicals.

But Holmer said they had no "hot" information pointing to these groups. He described the broad investigation thus far as "the typical situation in the moment when you start a big murder case. You have to be both patient and impatient."

While the crime rate has been steadily rising in Sweden, murders are still relatively rare. One police official said "20 or 25" homicides are committed each year in Stockholm, five or six of them with guns, although he could not remember the last one before Palme's killing. [By comparison, the Discrict of Columbia registered 148 homicides last year and 178 in 1984.]

Outside Stockholm police headquarters, workers today sifted through huge bins of garbage gathered from containers in the vicinity of the shooting in the hope of discovering a discarded weapon.

The most important clue thus far appears to be the "peculiar" design of the two lead-sheathed, copper-tipped bullets that were fired. In their own reference collection of 600 different types of bullets, Holmer said, "we have none that is similar."

Shortly after the killing, the police found one of the bullets about 40 yards from Palme's body. This bullet, they said, apparently was the second of the two fired and had slightly wounded Palme's wife. The fatal bullet, which hit Palme in the upper back and exited his body, was found today in a pile of snow and debris that police had gathered from the sidewalk where Palme fell.

Police have theorized that the killer followed the Palmes Friday night when they left their home at 8:40 and traveled by subway to the movies. "We reckon that the murderer . . . waited, either inside or outside the cinema" while they watched the show, Holmer said.

The killer, he said, "then followed them" on foot about two blocks along a six-lane, busy boulevard, to where a pedestrian walkway met the street between two buildings. There, where vehicles could not follow, the killing took place.

Neither the killer, nor either of the Palmes, spoke before the shots were fired from a short distance, police said. The assailant fled up the walkway, which ends in several flights of stairs leading to a number of small streets.

At least one man, who the police have not identified but have implied was a passer-by, ran after the killer, but lost him at the top of the stairs, police said. At that point, a strolling couple also saw him briefly.

Swedish Foreign Ministry spokesman Lars Lonnback referred again today to Palme's desire for privacy, and his decision on Friday morning to dismiss his bodyguards for the rest of the day. "It is a fact that he on many occasions insisted on not having security guards," Lonnback said. "It seems to have been fateful to him, but that is a fact we have to accept."

Holmer said bodyguards now had been assigned to Carlsson and other political leaders.