A senator, his daughter and a British visitor were killed by antigovernment rebels last night at a ranch in southwestern Zimbabwe, a government spokesman said today.

Sen. Paul Savage, 70, a member of the Republican Front party of former prime minister Ian Smith, was the first member of Parliament killed in the violence that has swept through embattled Matabeleland province during the past year since opposition leader Joshua Nkomo was dismissed from the Cabinet.

The deaths, bringing to seven the number of whites killed in the area during the past two weeks, demonstrated that the rebels are continuing to operate despite a massive Army offensive in the province during the past two months in which about 1,000 civilians reportedly have died.

Government ministers toured the province during the Easter weekend telling rallies in the rural areas how the Army was stamping out the rebels and restoring order. They also warned the local people not to feed or give other support to them.

It would appear from last night's attack on the Savage farm, located about 80 miles south of Bulawayo, that the rebels are still getting support. The government spokesman said about 20 took part in the raid, a large number to hide and feed without local assistance, forced or voluntary.

The spokesman said the rebels chased the black workers off the farm and found the Savage family having a barbecue.

The rebels "ordered them to raise their hands," the spokesman said, and then opened fire, killing Savage, his daughter Colleen, 20, and the Briton, whose name is being withheld pending notification of relatives. Savage's wife was also seriously wounded, but a hospital official said she is out of danger.

The raiders then ransacked the house and stole "a large quantity of property," including a Land Rover, the spokesman said.

The Savage farm was near Gwanda in the south of Matabeleland, more than 100 miles away from areas in the north of the province where most of the dissident violence and Army counterattacks have taken place.

Five weeks ago the Gwanda region was safe enough for the government to take a group of Zimbabwean reporters on a tour intended to refute foreign press reports of Army brutalities.

The problem for the Army is that the rebels operate in a vast, mainly arid area of almost 20,000 square miles, making it difficult for the troops to cover the entire area without getting local support.

The rallies this weekend, in which the government tried to win over the people in Nkomo's tribal stronghold, demonstrated the difficulties Prime Minister Robert Mugabe faces following the Army offensive.

At a rally Saturday in Gwelutshena, 120 miles northeast of Bulawayo, Enos Nkala, minister of national supplies, and Emmerson Munangagwa, the minister in charge of security, exhorted a mainly passive crowd of about 1,500 persons to back the government efforts to wipe out the rebels.

The crowd was generally silent except when Nkala announced that the abolition of the dusk-to-dawn curfew, the reopening of stores and the resumption of bus services and drought relief. That brought prolonged cheers from the people; the services had been cut off since the start of the Army sweep in January.

Some people in the crowd told reporters that they were bitter about the Army killings and had been forced to come to the rally. A colonel, who declined to be named, denied the allegations, however, and said the Army and the people had good relations.

More than 5,000 troops formerly loyal to Nkomo, who fled to London last month, are known to have deserted the Army during the past year. Many are believed to have become common criminals who attack without any political motivation.

It is unknown how many rebels are seeking the political restoration of Nkomo and the release of his former senior military men now standing trial for allegedly stashing arms. Some westerners estimate that the number may be as low as 500.

About a dozen whites, mainly farmers, have been victims of the rebels since Christmas. They apparently are being targeted in an effort to drive them off the farms since the whites are responsible for the bulk of agricultural production in the country.

The guerrillas used the same tactics during the bitter seven-year war against white-minority rule.

During the past few months, the farmers have complained to the government about their security and have been reissued Army weapons.

Few farmers have left, although some located close to Bulawayo have moved into the city and commute to their farms.

So far, there has been little impact on overall farm output since little of the prime agricultural land is in Matabeleland, which is mainly a cattle-raising area. The rest of the country is generally peaceful.