The South African government admitted today that it transferred $11.5 million to a secret Swiss bank account in 1974 in an effort to buy the Washington Star as part of a miltimillion-dollar covert propaganda campaign to gain influence abroad.

The government account of the attempt, presented in Parliament today, is the first oficial response to press reports here last October alleging that the government made $11.5 million available to conservative Michigan publisher John McGoff. McGoff tried unsuccessfully to buy The Star in 1974 and 1975.

Today's report, prepared by a government investigating commission looking into allegations of misuse of South African funds, was issued as accusations increased that present high officials were involved. The commission, however, reaffirmed its earlier finding that no present Cabinet members had a role in any wrongdoing.

The report did not say who received the money for the "highly secret" project to buy The Washington Star and McGoff has previously denied the allegations.

(An offical at McGoff's headquarters said Monday night that McGoff and his spokesmen were not available to comment on the new report.)

The South African government investigators said that the $11.5 million was transferred from the Defense Department budget on the order of Nicolaas Diederichs, then finance minister.

Investigators said the money was sent to the Union Bank in Switzerland "to enable the former department of information to purchase the 'Washington Star' in the U.S.A." The report did not say what happened to the money after that.

In an interview, however, a well-placed source here said McGoff was the conduit for the money.

After McGoff's initial unsuccessful effort to buy The Washington Star, it was purchased, in 1974, by Texas millionarie Joe L. Allbritton. Allbritton sold it to Time Inc. a year ago.

According to the investigators' report, Prime Minister Pieter W. Botha, then defense minister, objected to the transfer of money from his department but was not aware of what the money was to be used for.

An investigation is continuing into whether all the money has been returned to South Africa, the official report said. According to newspaper reports here, McGoff used some of that money, after the Star bid failed, to buy a California newspaper, the Sacramento Union. The investigators made no mention of that today.

The admission of the attempt to buy the Washington daily is likely to trigger U.S. Justice Department inquiries into whether the South Africans or their American partners violated any of the laws that require foreign government money transfers to be registered with the U.S. government.

The investigate report was ordered by Botha to quell the controversy surrounding his government as allegations mount that he has tired to cover up the scandal, involving the possible misuse of millions of dollars by top South African officials.

Increasingly, the scandal's political repercussions are presenting Botha with the possibility of having to hold an early election. That could allow the conservative wing of the ruling National Party to gain the upper hand and force Botha to abandon his plans for a new constitutional arrangement that would share some power with Indians and coloreds (people of mixed race) at the national level.

The three-man judicial commission headed by Judge Rudolph Erasmus, which prepared the investigative report today reaffirmed conclusions it released in December that none of the present Cabinet ministers had a part in the financial abuses of the now-defunct Information Department, including the covert funding of the progovernment newspaper, The Citizen.

The Erasmus Commission, however, said it would be ready to amend these conclusions if new evidence came to its attention in the future.

Today's developments are unlikely to halt the widening crisis for the government, because there is no explanation for discrepancies between the report's conclusions and allegations by two former government officials implicating the current finance minister and President John Vorster in the Citizen project.

The probers skirted the controversial issue of Vorster's responsibility in the Citizen scheme, which cost the state $36 million, by saying that since Vorster is not a Cabinet minister, he is not within the scope of their investigations for this report.

In December the investigators cleared Vorster, who was prime minister at the time, of any responsibility for The Citizen, accepting his word that he learned of it belatedly in August 1977, almost 20 months after the concept was initiated.

But former information secretary Eschel Rhoodie and former information minister Cornelius Mulder have both charged that Vorster knew of the newspaper funding project from its inception in December 1975. Mulder and Rhoodie were blamed by the Erasmus Commission last December for The Citizen and for other financial irregularities in the former Information Department.

The opposition has already initiated impeachment proceedings against Vorster on the ground that he knew of the Citizen funding last May when Mulder denied to Parliament that there was any government money in the paper.

But Vorster, who moved to the ceremonial post of president last September, is in little danger of being removed from office through impeachment since the procedure requires far more than the 27 seats the opposition parties supporting impeachment have in Parliament.

Mulder made his charges against Vorster and Finance Minister Owen Horwood a week ago.

Today, the investigators' report spoke derisively of Mulder: "The commission could not condemn Sen. Horwood on suspicion alone, especially where it was aroused by the allegations of Dr. Mulder, who admitted that as minsiter he told Parliament a lie," the report said.