The governor of South Africa's central bank, Gerhard de Kock, broke three days of silence on his emergency mission through western financial capitals and acknowledged yesterday that the future of the country's troubled economy depends on progress toward political change.

"The world has a certain perception of South Africa's political problems, and they are concerned that if South Africa cannot solve these problems fast enough, South Africa's economy will suffer. This perception . . . can only improve if South Africa takes the right steps."

De Kock made his remarks in a 15-minute interview with the South African Broadcasting Corp. shown on South African television last night. De Kock canceled a press conference in Washington scheduled for yesterday before he left the city Monday.

Underlining how the continuing violence has damaged confidence in the economy, the South African rand dropped sharply yesterday on foreign exchange markets, closing at 42 U.S. cents, down from 45.5 Monday.

The rand's decline suggested that Sunday's emergency financial measures, which included a four-month freeze on payments of principal on $12 billion in short-term foreign debt and imposition of exchange controls, would not be enough to restore confidence in the country's economy, analysts said.

Acknowledging the political dimension to the country's financial crisis, de Kock said he was optimistic about the future of the South African economy, "on condition that South Africa makes progress towards a solution to her political problems."

De Kock held private meetings over the weekend with the chairman of the Federal Reserve Board, Paul Volcker, and senior State Department officials, it was officially confirmed yesterday.

There was no official comment on the talks, but administration sources said de Kock met with Volcker in New York Saturday and on Sunday with Michael H. Armacost, undersecretary for political affairs and Frank G. Wisner, deputy assistant secretary, at the State Department.

The fact that de Kock appeared to meet with a cool reception in Washington was seen as indicating the Reagan administration's reluctance to become too involved with his mission. An administration official said Sunday: "We want to stay out of this as much as we can."

In the interview, de Kock continued to cast his mission in positive terms, saying he had met with "understanding" during his talks with bankers and monetary officials in Washington and New York, where he met Friday with officials at Citibank and, yesterday, with E. Gerald Corrigan, president of the Federal Reserve Board of New York.

De Kock denied that he had sought talks with bankers in order to borrow money, saying that he had visited western financial capitals to explain the reasons behind Sunday's decision to freeze until the end of the year repayments of principal on foreign debt. South Africa has said it will continue to pay interest on the debt.

De Kock described the move as a "standstill" rather than a debt moratorium.

The governor drew a sharp distinction between the debt problems of Latin American countries and those of South Africa, which he described as only "temporary." He said that South Africa had not overborrowed externally or overspent internally and was fully prepared to honor its international obligations.

Until the financial crisis that came to a head with the collapse of the rand and the emergency measures announced Sunday, South Africa had the soundest credit standing in Africa.

Banking sources said yesterday that South Africa's unilateral repayment freeze poses a dilemma for its international creditors. Faced in the past with the possibility of a sovereign country failing to meet its debt obligations, banks have agreed to form a steering committee to agree on rescheduling terms.

"In this case, the political factors are overriding, and they will be very reluctant to be seen to be entering negotiations with the South Africans; on the other hand, they all want their money back," said one senior American banker.

South Africa has said it will appoint a senior individual banker to act as an "honest broker" between Pretoria and the banking community, a move that could help negotiations. But analysts said yesterday that a successful agreemenet on rescheduling would depend on the caliber of the meditator.