* EM FX index at seven-month highs, stocks extend gains

* China's August industrial output, retail sales surge

* Yuan at 16-month high

* Turkish lira flat vs dollar; Ankara sees no EU sanctions

* Polish cenbank policy decision awaited

Sept 15 (Reuters) - Emerging market currencies reached seven-month highs on Tuesday as upbeat economic data from China pushed the yuan to a 16-month peak, while Turkey's lira remained near record lows amid tensions in the eastern Mediterranean.

Keeping hopes for a steady economic recovery alive, China's industrial output accelerated the most in eight months in August, while retail sales grew for the first time this year.

A dip in the U.S. dollar ahead of the Federal Reserve's policy announcement on Wednesday also boosted emerging market currencies, pushing MSCI's index of developing world currencies 0.3% higher. Its stocks counterpart rose half a percent, extending gains to a third straight session.

The yuan firmed 0.4%, taking gains this year to around 2.6%. But analysts warned against being over optimistic as trade tensions remain an issue between China and the United States.

"Tremendous uncertainties are ahead, which seems however unable to rattle the market for the time being. The market is split for now on whether the yuan could reverse the depreciation trend that is in place since 2015," said Hao Zhou, an FX analyst at Commerzbank.

Turkey's lira touched new lows against a stronger euro , while against the dollar it was about 0.4% away from record lows. Moody's downgrade of Turkey's credit rating had weighed on the currency on Monday.

Tensions with Greece over energy resources in the Mediterranean have also pressured the currency, which is down about 20% so far this year.

Ankara does not expect to face European Union sanctions over the dispute, Foreign Minister Mevlut Cavusoglu said on Monday, a day after a Turkish survey ship pulled out of contested waters.

The South African rand firmed 0.3% with all eyes on the central bank's decision on Thursday, while Russia's rouble made muted gains as oil prices fell.

The Polish zloty was flat against a stronger euro ahead of a central bank meeting later in the day. Commerzbank's Tatha Ghose expects no change in monetary policy.

"Had manufacturing growth kept collapsing in latest readings, and had inflation dropped towards deflation, the central bank might have looked for monetary easing via additional quantitative easing programmes," he said.

"But, this is not the situation."

In Budapest, stocks slid 1% in what could be their biggest drop in two weeks after data showed Hungary's construction sector output plunged by an annual 21% in July, posting its biggest fall in four years.

Real estate company Budapesti Ingatlan Hasznositasi es Fejlesztesi Nyrt was the biggest decliner, down 4.2%.

For GRAPHIC on emerging market FX performance 2020, see http://tmsnrt.rs/2egbfVh For GRAPHIC on MSCI emerging index performance 2020, see https://tmsnrt.rs/2OusNdX

For TOP NEWS across emerging markets

For CENTRAL EUROPE market report, see

For TURKISH market report, see

For RUSSIAN market report, see (Reporting by Susan Mathew in Bengaluru. Editing by Jane Merriman)