* EM stock index slides for fourth straight session

* Lira firms to 11.1 a dollar

* Polish zloty at 12-year lows amid Belarus migrant crisis

* Brussels considers withholding funds from Poland and Hungary

Nov 22 (Reuters) - Emerging market shares fell for a fourth straight session on Monday as rising COVID-19 cases in Europe and some hawkish comments from the U.S. Federal Reserve weighed on risk appetite, while Turkey's lira firmed after plumbing record lows.

MSCI's index of EM shares hit a two-week low, down 0.4%, with Hong Kong, India and Taiwan bourses pulled lower by tech names. Losses outside Asia included Russia and Middle East .

Mainland China stocks, however, rose on policy easing expectations.

Austria's fourth national lockdown to stem COVID-19 infections, and Germany warning it may follow suit, had investors worried about the economic fallout.

Meanwhile, Fed policymakers such as Vice Chair Richard Clarida and Governor Christopher Waller are publicly debating whether U.S. stimulus should be tapered faster as inflation surges.

Massive stimulus from major central banks had helped inflows into emerging market assets through the COVID-19 pandemic. With many EM central banks hiking rates aggressively, interest rate differentials with developed markets had kept EM currencies attractive for carry trade.

But rate hikes in the United State could reduce that appeal.

"If tapering seems more urgent now, that suggests that, not too late in 2022, the greenback will once again enjoy a positive carry," said Ulrich Leuchtmann, head of FX and commodity research at Commerzbank.

"That means we might see further U.S. dollar strength."

LIRA FIRMS

However, EM currencies broadly steadied on Monday after a painful week on the back of dollar gains, and growth and inflation concerns.

Turkey's lira firmed 0.7% to 11.1 per dollar after dropping almost 14% in the past 10 sessions. Data on Monday showed Turkish consumer confidence tumbled to record lows, reflecting the pain of the lira selloff to all-time lows.

The Russian rouble firmed with oil recovering from seven-week lows. But the Kremlin's accusation that Western nations were whipping up tensions in Ukraine kept sentiment in check.

In central and eastern Europe, the Polish zloty was not far off 12-year lows hit on Friday against the euro.

Polish Prime Minister Mateusz Morawiecki warned on Sunday that the migrant crisis on the Belarus border may be a prelude to "something much worse", and Poland's border guard said Belarusian forces were still ferrying migrants to the frontier.

Meanwhile, the European Commission has started a long-awaited probe into whether Poland and Hungary should continue to receive billions of euros from the EU budget.

With consumer confidence in Hungary also sliding, the forint failed to capitalise on the euro's weakness.

For GRAPHIC on emerging market FX performance in 2021, see http://tmsnrt.rs/2egbfVh For GRAPHIC on MSCI emerging index performance in 2021, see https://tmsnrt.rs/2OusNdX

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For CENTRAL EUROPE market report, see

For TURKISH market report, see

For RUSSIAN market report, see

(Reporting by Susan Mathew in Bengaluru; Editing by Kevin Liffey)