Chinese investors seemed none too hopeful as Shanghai blue chips slipped 1.8%. That led MSCI's broadest index of Asia-Pacific shares outside Japan down 0.4%.
Japan's Nikkei dipped 0.2%, while E-Mini futures for the S&P 500 ESc1 edged down 0.18%.
Wall Street had been just as cautious with the Dow ending Monday up 0.03%, while the S&P 500 lost 0.17% and the Nasdaq 0.32%.
There are no less than five Fed policy makers speaking on Tuesday, including Chair Jerome Powell, and markets assume they will stick with the recent dovish message.
"It's always possible the chair could walk back some of the market's dovish interpretation of last week's FOMC meeting...but we suspect he will reinforce the message laid out last week," said Kevin Cummins, a senior U.S. economist at NatWest Markets. "By the end of July, we believe the Fed will have seen enough to decide that action to counter downside economic risks and low inflation/inflation expectations is warranted, and so we look for a 25 basis point rate cut at the next FOMC meeting."
Markets are running well ahead of that. Futures 0#FF: are fully priced for a quarter-point easing and imply a real chance of a half-point move.
A total 100 basis points of cuts are implied by mid-2020, a major reason two-year yields are well under cash at 1.745%.
Yields on 10-year Treasuries have dived 120 basis points since November and, at 2.01%, are almost back to where they were before Trump was elected in late 2016.
The speed and scale of the latest decline has seen the dollar fall for four sessions in a row against a basket of other currencies to stand at a three-month low of 95.937.
"USD DXY now looks likely to break through the March low of 95.76 and below there 95.0," said Tapas Strickland, a markets strategist at NAB.
"The drivers here continue to be heightened expectations of the Fed cutting rates - now 3.1 cuts priced by years' end," he said, noting that a number of index trackers showed the data flow from the United States was now showing more disappointing misses than Europe.
The euro has climbed to its highest in three months and was last holding firm at $1.1403, within striking distance of the March top of $1.1448.
Against the safe-haven yen, the dollar has hit its lowest since the January flash crash and was last at 107.06 yen.
The pullback in the dollar combined with lower yields globally has put a fire under gold, which touched a six-year top. The metal is up 12% since early May at $1,1425.02 an ounce, with the next target the 2013 top of $1,433.
Oil prices lost some ground on Tuesday, after rising sharply last week in reaction to tensions between the United States and Iran.
Brent crude futures eased 51 cents to $64.35, while U.S. crude fell 51 cents to $57.39 a barrel.
(Editing by Simon Cameron-Moore) ((Wayne.Cole@thomsonreuters.com; 612 9321 8162; Reuters Messaging: email@example.com))
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