MSCI's broadest index of Asia-Pacific shares outside Japan was 0.1 per cent firmer at 549.71 points, not far from a 10-year high of 554.63 set last week.
Australian shares also edged higher and back toward a five-and-a-half-month peak touched on Monday, while Japan's Nikkei fell 0.2 per cent from a 21-year high.
"Despite a lack of any real movement in markets, we know there are landmines and event risk to work through and this creates opportunity for short-term traders," said Chris Weston, chief strategist at IG Markets.
"Whether the gains can continue this week is obviously yet to be seen. I remain a bull, but of the view that these markets are tired, fatigued and need new information to fuel the beast."
In the United States, the Dow Jones Industrial Average fell 0.23 per cent, the S&P 500 lost 0.40 per cent and the Nasdaq Composite slipped 0.64 per cent.
Corporate results will dominate near-term sentiment with earnings from General Motor, McDonald's, and Lockheed Martin due later in the day.
European STOXX 600 shares rose 0.16 per cent, although Madrid's bourse IBEX shed 0.6 per cent as Spain's crisis entered another week.
Madrid took the unprecedented step of firing the government of Catalonia on Saturday in a last resort to thwart its push for independence. Catalan leaders called for civil disobedience in response.
In Germany, the Alternative (AfD) party is set to clash with other parties over its nomination for a senior parliamentary post when the Bundestag meets on Tuesday.
The political tensions have weighed on the euro which hovered near two-week lows at $1.1752. The market is on edge ahead of a European Central Bank (ECB) meeting on Thursday where it is expected to announce some form of policy tapering.
Investors were also biting their nails as suspense builds over who might be the next chair of Federal Reserve after Janet Yellen's term expires in February.
US President Donald Trump has indicated an announcement is expected "very shortly".
The market is betting on Federal Reserve Governor Jerome Powell as the likely choice while Mr Trump is also weighing on Stanford University economist John Taylor and current Federal Reserve Chair Janet Yellen.
The dollar index inched lower to 93.8 but stayed in sight of a recent two-month peak.
The New Zealand dollar rose 0.2 per cent from near five-month lows with investors focused on any policy tidbits out of the country's new Labour government.
In commodities, spot gold was mostly unchanged at $1282.26 an ounce.
Oil prices were little changed as supply disruptions in Iraq dented exports by OPEC's second-largest producer and US drilling rates showed a slowdown.
Brent crude added 6 cents to $57.43, while US crude rose 3 cents to $51.93 a barrel.