Government forces and guerrillas have clashed in the Rhodesian capital of Salisbury for the first time in the country's six-year-old civil war, the Rhodesian police announced yesterday.

The official police communique gave few details except to say that three guerrillas had been killed Saturday in a gun battle with police in the all-black Highfield Township. Two others were reported captured and wounded in separate incidents in Highfield and Mufakose townships.

The communique reported that the five were armed with grenades and automatic weapons.

Highfield is five miles from the center of Salisbury and a mile from the nearest white suburb.

Highfield residents reported that the house in which three of the guerrillas were killed was riddled by more than 2,000 rounds of ammunition.

The government announcement confirmed sketchy reports over the weekend that slipped through the heavy censorship of the Rhodesian military command. It also underscored the increasing boldness with which guerrillas are operating in Rhodesia and the declining control the white government exercises, even in its back yard.

The incidents followed reports last week that a guerrilla assassination squad from the Zambia-based army of nationalist leader Joshua Nkomo had crossed into Rhodesia in June and was hiding somewhere in Salisbury.

The six-man squad was reportedly on a mission to kill leading black figures in the controversial internal settlement with the white government of Prime Minister Ian Smith, which Nkomo and his Patriotic Front ally, Robert Mugabe, oppose.

Those reports were based on the statements of Reuben Danga, 22, allegedly a captured guerrilla, who appeared at a government press conference.

Despite the press conference, Rhodesian newspapers were forbidden to report Danga's statements, and the joint military command, which has heavily censored the copy of foreign correspondents since January, apparently deleted references to Danga's story from outgoing dispatches.

The Rhodesian government, normally reluctant to give much detail to the press, has become even touchier in the past seven months. Saturday, for example, it announced that 39 civilians had been killed two weeks before, but gave few other details.

Black sources in Salisbury then said that the 39 had been at a political rally for Rev. Ndabaningi Sithole, one of the blacks in the interim government. They said that the victims had been slain and left by the guerrillas for other blacks to see.

Military censors review the copy of all correspondents and sometimes delete material that reporters contend is unrelated to military matters.

They have previously insisted on deflating journalists' estimates of the number of guerrillas in Rhodesia, and only recently have government press spokesmen conceded that more whites have emigrated from the country than they had originally admitted.

Highfield, considered the most politically active of Salisbury's black townships, is the bedrock of urban black support for Bishop Abel Muzorewa, considered to be the most popular of the black leaders in the interim government.

Muzorewa, in an interview with The Washington Post last week, denied reports that the guerrilla war has intensified since he, Sithole and Chief Jeremiah Chirau signed the internal settlement with Smith last March.

But accounts from Salisbury say that guerrillas inside Rhodesia, now estimated variously to number between 7,000 and 10,000, are operating with growing impunity.

Yesterday's report coincided with one from Lusaka, Zambia, Nkomo's base, that as many as 2,000 freshly trained guerrillas have been flown into Zambia from bases in Angola over the past month. This would bring the estimated strength of Nkomo's army to between 8,000 and 10,000 troops, most of them still believed to be in Zambia.

Smith threatened publicly last week that the internal agreement, which calls for black majority rule by the end of this year, would not be put into effect unless there is a cease-fire in the guerrilla war.

With increasing chaos in the countryside, there are questions over whether the inernal government will be able to hold elections for a majority-rule government anyway.

Smith had been assured earlier this year in negotiations with the black leaders that a settlement for majority rule would end the war, and officials of both the Sithole and Muzorewa delegations openly boasted that, through secret contacts with guerrillas, they could bring many of them home peacefully.

Despite a general amnesty offered by the biracial interim government, however, the war appears to be intensifying, and yesterday's report of the incidents in Salisbury tends to cast doubts on Muzorewa's contention that guerrillas are laying down their arms.

Last January, in a string of attacks within 10 days, guerrillas killed a dozen whites in the tranquil White Highlands farming areas within a 50-mile radius of Salisbury.

White Rhodesians, who center their lives on the country's half-dozen cities and were used to thinking of the guerrilla war as being out in the bush country, increased the number of roadblocks around Salisbury and spot security checks within the city itself.

The guerrillas, nevertheless, brought the war to Salisbury.