(Updates rand, adds bonds and stocks) JOHANNESBURG, June 3 (Reuters) - South Africa’s rand weakened on Thursday, stepping back from a more than two-year peak hit earlier in the session, as the dollar rose after stronger-than-expected U.S. private payrolls data that suggested an improving labour market. At 1506 GMT the rand was 0.59% weaker at 13.6050 per dollar, having touched 13.4975 earlier, its firmest level since February 2019. The earlier rally was mainly driven by growing appetite for riskier but high-yielding assets. “Growing bets that Fed monetary tapering may not be imminent drove a rotation out of the USD and into higher-Beta currencies such as the ZAR, with the high real yields SA offers still proving to be too enticing to ignore,” said economists at ETM Analytics. U.S. Federal Reserve officials have repeatedly said the bank would look to keep lending rates low for some time, insisting that current price pressures were temporary. Low rates in the United States and other developed economies have benefited high-yielding currencies like the rand that offer higher returns. Some traders opted to pocket gains, with closely watched U.S. jobs data due on Friday, which should offer further clarity on whether the faster-than-expected pace of economic recovery can be sustained and what that might mean for monetary policy. South Africa will also release first-quarter economic growth data early next week. “A marginal degree of cautiousness appears to be setting in,” said the ETM analysts. Stocks on the Johannesburg Stock Exchange (JSE) slumped on Thursday paring most of the gains seen last week as strong U.S. data overshadowed economic recovery sentiments with worries of impending inflation. Rising inflation could force the U.S. Federal Reserve to withdraw support for the economy by increasing rates. Analysts have said that since a majority of the South African stock market is linked to global markets, worries of higher inflation and interest rates push the market down, in line with most global markets. The benchmark all-share index closed down 1.82% to 67,791 points and the blue-chip index of top 40 companies ended down 1.93% at 61,573 points. Government bonds firmed, and the yield on the benchmark instrument due in 2030 was down 3 basis points at 8.855%. (Reporting by Mfuneko Toyana, Olivia Kumwenda-Mtambo and Promit Mukherjee; Editing by Steve Orlofsky) Our Standards: The Thomson Reuters Trust Principles.