JOHANNESBURG, Sept 21 (Reuters) - The South African rand fell to more than three-week lows on Tuesday, hurt by subdued risk appetite and after ratings agency Fitch said Africa's most industrialized economy will continue to face challenges as it seeks to stabilize debt.

At 1500 GMT, the rand was trading at 14.8730 against the dollar, 0.6% weaker than its previous close.

The currency has been hit this week by the fallout especially on emerging markets from Chinese property firm Evergrande's debt debacle, a rout in commodity prices and a stronger dollar.

On Tuesday, Fitch said even though stronger-than-expected fiscal revenue in recent months meant that South Africa's budget deficit will be smaller than earlier Treasury projections, the government would still face challenges to stabilize debt.

Affirming South Africa's rating at ‘BB-’with a negative outlook in May, Fitch indicated that progress on fiscal consolidation that boosts confidence that government debt/GDP stabilization would be achieved could be a trigger for positive rating action.

"However, even if the deficit is lower than anticipated in FY21/22, it is unclear whether this outperformance will be sustained," Fitch said in Tuesday's statement, adding that notably, mining revenue will slow as commodity prices becomes less supportive.

Looking ahead, the U.S. Federal Reserve meeting due to conclude on Wednesday will be critical for all emerging market currencies as a tapering of its stimulus measures would likely prompt a flight of capital to the dollar.

The South African Reserve Bank's monetary policy meeting on Sept. 23 will also be a key event for the local currency.

Stocks rose, rebounding alongside commodity prices after the previous day's heavy selling.

The Johannesburg Stock Exchange's Top-40 Index climbed 1.5% to 56,086 points and the broader All-Share Index was up by almost the same amount to 62,362 points.

Among the biggest gainers of the day on the blue-chip index were petrochemicals producer Sasol and gold miner AngloGold Ashanti, both up around 4.5%.

In fixed income, the yield on the government bond due in 2030 was up a single basis point to 9.065%. (Reporting by Promit Mukherjee and Olivia Kumwenda-Mtambo; Editing by Emelia Sithole-Matarise)