MSCI's broadest index of Asia-Pacific shares outside Japan firmed 0.1%, after notching its highest close since June 2018. Japan's Nikkei added 0.2% to be near its highest in 15 months.
Chinese shares opened firm with the blue-chip CSI300 index up 0.2%.
Australia's main index scored another all-time peak and South Korea was near its best level since October 2018. E-Mini futures for the S&P 500 ESc1 edged up 0.1%.
Eyes will be on U.S. corporate earnings with Netflix Inc, Intel Corp and Texas Instruments Inc set to report this week, while central banks in the European Union, Canada and Japan hold policy meetings.
Sentiment was supported by the relentless run of record highs on Wall Street. Only three weeks into the new year, the S&P 500 .SPX has gained just over 3% and the NASDAQ almost 5%.
Ray Attrill, head of foreign exchange strategy at National Australia Bank, suspects the strength on Wall Street owes much to the Federal Reserve's decision in September to rein in rising repo rates by flooding markets with cash.
"The relationship between the size of the Fed's balance sheet, now some 11% bigger than where it was in late September, and the performance of U.S. risk assets is uncanny," he said, noting the balance sheet had just hit a three-month top of $4.18 trillion.
Analysts at BofA Global Research noted global stock market capitalisation had ballooned by $13 trillion since its September lows and the S&P was only 5% away from marking the biggest bull run in history.
"We stay irrationally bullish until peak positioning and peak liquidity incite a spike in bond yields and a 4-8% equity correction," they said in a note.
The Fed's buying binge on Treasury bills has kept bonds bid even as stocks surged and economic data stayed healthy. Yields on two-year notes are dead in line with the overnight cash rate at 1.56%, compared to 2.62% this time last year.
The string of mostly solid U.S. data has underpinned the dollar, particularly against the safe-harbour yen. The dollar stood at 110.19 yen on Monday, having hit an eight-month peak of 110.28 last week.
The euro was stuck at $1.1095, while sterling idled at $1.3000 after poor British economic news fanned speculation about a cut in interest rates.
Against a basket of currencies, the dollar was flat at 97.616, moving away from the recent trough of 96.355.
Spot gold stood at $1,557.75 per ounce, having hit a seven-year top earlier this month of $1,610.90 at the height of Iran-U.S. tensions.
Concerns about a cut in supply from Libya sent oil prices higher.
Brent crude LCOc1 futures rose 76 cents to $65.61 a barrel, while U.S. crude CLc1 jumped 61 cents to $59.15.
(Reporting by Wayne Cole; additional reporting by Swati Pandey; Editing by Christopher Cushing & Shri Navaratnam) ((Wayne.Cole@thomsonreuters.com; 612 9321 8162; Reuters Messaging: firstname.lastname@example.org))
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