Nov 18 (Reuters) - Emerging markets stocks were steady in cautious trade on Friday, and currencies on course to snap a three-week winning run, after hawkish commentary from the U.S. Federal Reserve dented sentiment.

St. Louis Fed President James Bullard said interest rates might need to hit a range from 5% to 7% to be "sufficiently restrictive" to curb inflation. This saw traders start to price in a higher terminal rate, likely over 5%.

MSCI's index of emerging market shares was flat, but was set to gain for the week in what would be its third straight week of gains. The around 0.7% rise for the week is a sharp departure from gains of more than 4% over the last two weeks.

"The window around the peak terminal is assembling around 5%, and the time to arrive there is narrowing, so the market is increasingly pricing in that peak Fed hawkishness from here," said Stephen Innes, managing partner at SPI Asset Management.

On Friday, bourses in the EM world were mixed with China, Taiwan and central Europe marking losses, while Turkish and South African assets gained.

Among currencies, against a slightly weaker dollar, China's yuan firmed 0.4% even as COVID cases rose. Beijing further relaxed COVID-19 rules, removing limits on the numbers allowed at theatres and events such as concerts and music festivals in low-risk areas without outbreaks.

"China is unlikely to be a straight-line market recovery, and the headline risk remains around COVID jitters, which adds to the reopening timeline confusion," Innes said.

Meanwhile, China's central bank introduced measures to make the market attractive for foreign investors.

Moves in other currencies were limited. MSCI's index of EM currencies was set to drop about 0.5% this week after gaining about 3% over the last three weeks.

South Africa's rand firmed against the dollar, while most central European currencies rose against euro.

South Africa awaits sovereign credit rating reviews by S&P Global and Moody's later in the day. Eyes next week will be on an interest rate decision by the South African Reserve Bank on Thursday as well as the release of October inflation figures.

ETM Analytics said in a research note it expected S&P and Moody's to leave South Africa's ratings and outlooks unchanged.

Some Asian units such as the Indian rupee, Malaysian ringgit and Indonesian rupaiah fell around 0.2% each. Mexico's peso lost 0.1%. For GRAPHIC on emerging market FX performance in 2022, see http://tmsnrt.rs/2egbfVh For GRAPHIC on MSCI emerging index performance in 2022, see https://tmsnrt.rs/2OusNdX

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For CENTRAL EUROPE market report, see

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For RUSSIAN market report, see (Reporting by Susan Mathew in Bengaluru; additibal reporting by Nellie Peyton; editing by Barbara Lewis)