With Wall Street and London closed for public holidays, there were few catalysts to drive business, though comments from top European Central Bank officials reinforced optimism that borrowing costs in the eurozone will come down at its June meeting.
Figures last Friday showing US consumer confidence picking up and inflation expectations coming down provided traders enough confidence to propel hopes for at least one interest rate cut before January.
That has put a little downward pressure on the dollar against its major peers, with the yen also supported by growing speculation the Bank of Japan will hike borrowing costs again within the next few months.
The main focus on trading floors, however, is Friday's release of the US personal consumption expenditures (PCE) index -- the Federal Reserve's preferred gauge of inflation, which is forecast to have seen a slight slowdown in April from the previous month.
The reading comes after a number of monetary policymakers warned in recent weeks that they were cautious about cutting rates too soon and wanted to see more data proving price pressures are easing.
The next couple of days will see fresh comments from more central bank officials that investors hope will shine a light on their thinking.
While the Fed continues to debate when to move on rates, the ECB appears set to make a cut with chief economist Philip Lane telling the Financial Times that "barring major surprises" the next direction will be downward.
That comes after eurozone inflation data for May, which is due Friday.
Hong Kong, Tokyo, Shanghai, Sydney, Seoul, Wellington, Manila and Bangkok fell, though Singapore, Taipei and Jakarta edged up.
London fell as investors returned from a long weekend break, while Paris and Frankfurt rose slightly.
On currency markets the dollar fell as dealers eyed a Fed reduction, even as the ECB and Bank of England consider moving before.
"The dollar is weaker across the board with the risk-positive backdrop seemingly overriding the greenbacks safe-haven appeal," said National Australia Bank's Rodrigo Catril.
Oil prices rose further ahead of a June 2 meeting of OPEC and other major producers that is tipped to see them maintain output cuts, while the start of the so-called US driving season is expected to see a lift in demand.
"A confluence of factors suggest some upside sensitivity in oil -- from fraught geopolitics to inventory drawdown to OPEC's assumed preference to maintain curbs," said Mizuho Bank's Vishnu Varathan.
- Key figures around 0715 GMT -
Tokyo - Nikkei 225: DOWN 0.1 percent at 38,855.37 (close)
Hong Kong - Hang Seng Index: DOWN 0.1 percent at 18,814.59
Shanghai - Composite: DOWN 0.5 percent at 3,109.57 (close)
London - FTSE 100: UP 0.2 percent at 8,331.67
Dollar/yen: DOWN at 156.80 from 156.82 yen on Monday
Euro/dollar: UP at $1.0875 from $1.0857
Pound/dollar: UP at $1.2777 from $1.2774
Euro/pound: UP at 85.13 from 85.01 pence
West Texas Intermediate: UP 1.4 percent at $78.77 per barrel
Brent North Sea Crude: UP 0.1 percent at $83.14 per barrel
New York - Dow: Closed for a holiday
dan/dhw
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