JOHANNESBURG (Reuters) - South Africa's rand firmed against the dollar early on Tuesday as the euro edged up to the greenback, while stocks pointed to a higher start. The JSE's blue chip Top-40 March futures contract went up 0.33 percent ahead of the market opening at 0700 GMT. The rand was trading at 7.69 to the dollar at 0638 GMT, 0.77 percent firmer than the close of 7.75 in New York on Monday. "The rand is starting off slightly stronger. We are starting to see the market levelling out after the huge move of last week. The euro (is) the main driver, it strengthened slightly overnight," said Brigid Taylor, a trader at Rand Merchant Bank. The rand touched a three-month low of 7.8560 on Friday last week but was rebounding in line with the euro, the currency of one of South Africa's big trading partners. Taylor said the rand was likely to trade between 7.65 and 7.78 to the dollar on the day. Investors remain cautious of risk-taking ahead of a European Union economic summit on Thursday, amid worrying fiscal health of some euro zone countries. Government bonds steadied, with the yield on the 2015 bond unchanged from Monday's closing level of 8.37 percent and the 2036 yield was also flat at 8.97 percent. Dealers will also watch local unemployment data at 0930 GMT to see whether jobs are being created after the economy exited a recession -- which wiped out about a million jobs -- in the third quarter of 2009. "A positive number will be a pleasant surprise for the market" said RMB's Taylor.