* MSCI Asia ex-Japan -0.3%
* European shares expected to fall
* Australian stocks rise after RBA cash rate cut
* Asian stock markets: tmsnrt.rs/2zpUAr4
By Andrew Galbraith
SHANGHAI, June 4 (Reuters) - Asian shares fell on Tuesday as weak economic indicators and an intensifying Sino-U.S. trade war inflamed concerns about global growth, supporting safe-haven assets such as bonds.
European equities are also expected to fall. In early European trade, pan-region Euro Stoxx 50 futures were down 0.36% at 3,279, German DAX futures fell 0.31% to 11,745, FTSE futures eased 0.27% to 7,155.5, and France's CAC 40 futures lost 0.53% to 5,193.
Investor focus has shifted to monetary policy this week with Australia's central bank cutting its cash rate to a record low on Tuesday, and India tipped to ease on Thursday.
Comments from the Federal Reserve on Monday, meanwhile, raised expectations the U.S. central bank is moving closer to a rate cut, as did a closely watched U.S. factory survey.
"Unless there's a circuit breaker, and it may come in terms of a Fed cut, or it may come in terms of more Chinese stimulus or the European Central Bank later this week...equity prices and bond rates are going to continue to go lower," said Greg McKenna, strategist at McKenna Macro.
The ECB holds its next policy meeting on Thursday and is expected to keep settings unchanged though there is growing speculation it could shift to a more dovish footing.
Losses across Asian equity markets on Tuesday followed falls on Wall Street overnight that saw the Nasdaq drop into correction territory. MSCI's broadest index of Asia-Pacific shares outside Japan was down 0.3%, after earlier rising as much as 0.18%.
The broad index was pulled lower by Chinese shares. China's blue-chip CSI300 index was 0.94% lower, and the Hang Seng lost 0.66%.
Defying the regional selloff, Australian shares finished 0.19% higher, boosted by the Reserve Bank of Australia's decision to cut its cash rate to 1.25%, a record low, in what could be the first in a series of stimulus measures.
Japan's Nikkei ended flat after a rocky session.
Underscoring slowdown concerns, a factory survey on Monday showed U.S. manufacturing growth eased in May to its weakest pace in more than two-and-a-half years, defying expectations for a modest rebound.
Hostile rhetoric between the United States and China continued on Monday as Washington accused Chinese negotiators of backpedalling on important elements of a trade deal that had been largely agreed by both sides.
Adding to broader investor worries are fears that U.S. antitrust regulators could target Alphabet, Facebook, Apple and Amazon.
News of U.S. government plans to investigate the tech giants dragged down tech shares on Monday, driving the Nasdaq 1.61% lower to 7,333.02. The drop took the index more than 10% lower than its May 3 closing record.
The S&P 500 lost 0.28% to 2,744.45 and the Dow Jones Industrial Average eked out a 0.02% gain to 24,819.78.
U.S. Treasury yields rose slightly on Tuesday but remained near recent lows. U.S. 10-year notes yielded 2.0882%, up from a U.S. close of 2.081%, having touched its lowest level since September 2017 on Monday.
The two-year yield rose to 1.8653% compared with a U.S. close of 1.84%.
The fall in the two-year yield reflects raised expectations of a more accommodative Fed.
St. Louis Fed president James Bullard on Monday said a rate cut "may be warranted soon" given risks to global growth posed by trade tensions and weak U.S. inflation.
Gold was up 0.12% at $1,326.47 per ounce, near three-month highs, and Japan's yen strengthened, with the dollar dropping 0.18% against the Asian safe-haven to 107.87.
"Risk aversion has also been seen with the yen carry trade unwinding as the markets comprehend that the U.S. technology containment strategy towards China is unlikely to reverse," analysts at Jefferies said in a note.
"In the short term, positioning has become so bearish that 'a ceasefire' could spark a risk rally."
The euro was 0.14% stronger at $1.1257, while the dollar index, which tracks the greenback against a basket of six major rivals, was barely changed at 97.134.
Crude prices whipsawed, resuming their declines after a brief bounce, on mounting trade worries.
U.S. crude was down 0.43% at $53.02 a barrel and Brent crude dropped 0.59% to $60.92 per barrel.
Reporting by Andrew Galbraith; Editing by Sam Holmes