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(Reuters) - Asian shares fell on Tuesday, weighed down by the prospect of further monetary policy tightening by central banks, China's renewed COVID outbreak and Europe’s energy shortage, which also left the euro a whisker from parity with the safe haven dollar.

MSCI's broadest index of Asia-Pacific shares outside Japan fell 0.8% to its lowest level in two years, while Japan's Nikkei lost 1.75%.

The euro fell as low as $1.0006 against the U.S. dollar, moving ever closer to parity for the first time since December 2002, as investors worry an energy crisis will tip the region into a recession.

“Risk-off sentiment is dominating global markets,” said Yuting Shao, macro strategist at State Street Global Markets.

"The dollar is the go-to international reserve currency. So when there is a recessionary risk or there's pickup of volatility, the greenback is the currency that people rush to because that is the safest," Shao added.

The dollar index, which tracks the currency against a basked of six peers rose to 108.47, the highest since October 2002.

The focus for this week will be macro data including the Consumer Price Index from the U.S. on Wednesday, and comments from Federal Reserve Officials as investors look for clues for the outcome of the Fed's upcoming policy meeting before officials enter the pre-meet blackout period.

A high inflation reading would add pressure for the Fed to step up its already aggressive pace of interest rate increases.

Also high on investors' list of worries is the fact multiple Chinese cities, including the commercial hub Shanghai are adopting fresh COVID-19 curbs starting from this week to rein in new infections after finding a highly-transmissible Omicron subvariant.

Additionally, the surging cost of energy in Europe is a major fear as the biggest single pipeline carrying Russian natural gas to Germany entered annual maintenance, with flows expected to stop for 10 days.

Investors are worried the shutdown might be extended because of the war in Ukraine, restricting European gas supply further and tipping the struggling eurozone economy into recession.

The yield on benchmark 10-year Treasury notes was at 2.9668% having dropped back below 3% overnight as investors bought safe haven Treasuries amid a sell-off on Wall Street.

The three major U.S. stock indexes ended lower on Monday on investor concerns about rising inflation and corporate earnings before the start of results season. International equities also largely fell, as did oil prices and bond yields.

Growth fears were also weighing on oil, despite concerns about the tight supply.

U.S. crude dipped 1.14% to $102.9 a barrel. Brent crude fell to $106.04 per barrel

Gold was slightly higher. Spot gold was traded at $1,734.6434 per ounce.

Asian stocks at lowest in two years, euro near par with dollar on growth fears

MSCI's broadest index of Asia-Pacific shares outside Japan fell 0.8% to its lowest level in two years, while Japan's Nikkei lost 1.75%.

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