By Selena Li and Xie Yu

HONG KONG (Reuters) – Asian shares and U.S. futures tumbled on Tuesday after a tumultuous Wall Street session, with investors nervous about the situation in Ukraine and eyeing the U.S. Federal Reserve amid worries about a move to tighter monetary policy globally.

NATO said on Monday it was putting forces on standby and reinforcing eastern Europe with more ships and fighter jets, in what Russia denounced as Western “hysteria” in response to its build-up of troops on the Ukraine border.

MSCI’s broadest index of Asia-Pacific shares outside Japan shed 1.2%, falling to its lowest in a month, and Japan’s Nikkei skidded 2% to its lowest level since August.

There were sharp declines around the region. Hong Kong lost 1.64% and Korea’s KOSPI fell 1.67%. The Australian benchmark tumbled 2.73% to hit an eight-month low, hurt also by a high inflation print Tuesday morning that stoked fears of approaching rate hikes Down Under. [AZN0236PW]

Asian markets were being dragged lower by concerns about faster U.S. rate hikes, mounting tensions over Ukraine, rising inflation and higher oil prices, said Carlos Casanova, senior economist at UBP.

“But on the upside, valuations are becoming more attractive and earnings growth are still robust for some sectors. So I think we will see a tug of war in the market for this week,” he said.

U.S. futures also fell in Asian hours, Nasdaq futures shed 1.2% and S&P500 futures lost 0.95%, after U.S. stock markets had recovered strongly late in the session to close higher, recouping steep losses made early in the day, as bargain-seeking investors snapped up shares.

The Dow Jones Industrial Average finished up 0.29%, the S&P 500 gained 0.28% and the Nasdaq Composite added 0.63%. [.N]

Keeping traders on their toes, the Federal Reserve will begin its two-day meeting later on Tuesday, with investors starting to speculate that there is a small possibility that they will announce a surprise rate hike.

Investors are also anxiously looking out for any hints about the timing and pace of rate hikes expected later this year. Money markets are priced for a first rate hike in March, with three more quarter-point increases by year-end.

However, U.S. benchmark Treasuries were sitting out some of the speculation. Yields on benchmark 10 year notes were at 1.76%, steady on the day, having finished a choppy day of trading Monday near where they started. [US/]

Singapore’s central bank also tightened monetary policy on Tuesday in an out-of-cycle move.

Market nerves sent the dollar higher against most peers. The dollar index was at 95.922, hovering near a two-week high, having gained 0.29% overnight. [FRX]

The Aussie dollar gained briefly after the high inflation print, but failed to hold on to its gains and the risk friendly currency was still hovering near the one-month low hit the day before.

Oil prices were also elevated, further worrying stock investors. U.S. crude rose 0.5% to $83.73 per barrel and Brent crude was at $86.83, up 0.65%. [O/R]

Gold held on to its recent gains as investors sought safety. The spot price was at $1,841 an ounce, flat on the day but near last week’s two-month high of $1,847.7. [GOL/]

(Reporting by Selena Li, Xie Yu and Alun John; editing by Richard Pullin)