* Hong Kong shares record best day in 10 months
* EM currencies rise as dollar dips on weak U.S. data
* Turkish lira, S.Africa rand jump 1%
By Medha Singh and Agamoni Ghosh
Sept 4 (Reuters) - Hong Kong stocks led a rally in emerging market shares on Wednesday after reports that the government may withdraw a controversial extradition bill, while upbeat Chinese data somewhat allayed fears over sluggish global growth.
The possible withdrawal of a bill that would have allowed extraditions to mainland China ushered in a sense of respite after months of unrest that has thrown the Chinese-administred city into its worst crisis in decades.
Hong Kong authorities have not confirmed the reports.
"It remains to be seen whether it will be enough to reverse the poison and mistrust between the people of Hong Kong and its executive, but it is at least a start," said Michael Hewson, Chief Market Analyst at CMC Markets.
Shares in the Hang Seng index jumped nearly 4%, helping MSCI's index for emerging market stocks to scale a fresh three-week high.
Further boosting sentiment was upbeat data from China reflecting the services sector's fastest expansion rate in three months in August, easing some concerns of a slowdown in the world's second largest economy.
Asian markets took heart from the positive data, with mainland Chinese shares closing at near five-week highs.
A similarly upbeat service sector report for August in Russia helped the country's stocks move higher, while a rise in oil prices pushed the crude exporter's currency higher.
Mumbai-listed stocks underperformed the broader market, after data showed that India's dominant services industry expanded at a slower pace in August.
Developing world currencies broadly rose after weak U.S. manufacturing readings dented the dollar.
Turkey's lira jumped 1%, continuing to take comfort from inflation figures released on Tuesday that are likely to pave the way for lower interest rates before year-end.
South Africa's rand hit a near four-week high following a better-than-expected jump in second-quarter economic growth and shrugging off the latest data which showed private sector activity contracted in August.
In emerging Europe, the Hungarian forint rose 0.5% against the euro to outperform its regional peers after data showed retail sales rose by an annual 6.4% in July after a revised 5.4% increase in June.
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For RUSSIAN market report, see (Reporting by Medha Singh and Agamoni Ghosh in Bengaluru Editing by Gareth Jones)