Jan 25 (Reuters) - Emerging market shares fell sharply for a third straight session on Tuesday as the threat of Russia-Ukraine military conflict and wariness over U.S. monetary policy weighed on sentiment.

Equity markets in Turkey, Hungary and Romania fell between 0.2% and 2.9% in volatile trade as the West stepped up preparations for its response to any Russian invasion of Ukraine.

But after a brutal European session on Monday, other markets were showing signs of stabilising. Russia's IMOEX share index climbed 1.2%, paring the previous session's near 6% slide, while those in South Africa and Poland firmed around 1.3% each.

"Markets are trading very nervously. At the moment, we're seeing increasing tensions being built up around Ukraine from both sides," said Jakob Christensen, chief analyst and head of EM research at Danske Bank.

"The next step to watch out for is the U.S. response to Russian demands," he said.

Given the rouble's slide - 4.7% this year - Christensen expects the Russian central bank to be slightly more hawkish in February and sees a 50 basis points interest rate hike.

Russia's rouble was 0.6% stronger at 78.6 a dollar after sliding to 14-month lows on Monday, while Ukraine's hryvnia edged 0.2% higher after its worst session in almost two years.

Russian OFZ bonds steadied, while hard-currency debt continued to fall on Tuesday.

The broader MSCI index of emerging shares fell 1.1% as investors braced for a hawkish Federal Reserve.

While a 25 basis point hike in March is fully priced in, there is plenty of market speculation about a rate raise as soon as Wednesday when the Fed concludes its two-day meeting.

Ahead of the Chinese New Year holidays, mainland shares lost more than 2%, while the yuan hit 3-1/2 year highs. Singapore's dollar outperformed regional peers after a surprise hike in interest rates.

With tech stocks down and North Korea firing what appeared to be two cruise missiles into the sea off its east coast on Tuesday, South Korea's KOSPI slumped to over one-year lows.

The EM index has lost about 1.8% this month but is nonetheless faring significantly better than MSCI's all-country index, which is down about 6% for the year with pressure coming from the high-value cluster that includes Apple , Amazon and Meta among others.

Hungary's forint was flat ahead of a central bank meeting later in the day when a 30 bps hike to 2.7% is expected, with inflation this year forecast at its strongest in a decade.

On Thursday, South Africa is seen hiking by 25 basis points to 4%.

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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(Reporting by Susan Mathew in Bengaluru; Editing by Kirsten Donovan)