MSCI's broadest index of Asia-Pacific shares outside Japan was slightly down in early trading, though Japan's benchmark Nikkei stock average added 0.5%.
Asian investors continued to monitor developments in Thailand, following news the army had declared martial law after six months of anti-government protests.
The declaration of martial law was intended to restore peace and order and does not constitute a coup, deputy army spokesman Colonel Winthai Suvari told Reuters.
Solid gains on Wall Street supported overall sentiment, with the S&P 500 gaining nearly 0.4% and the Nasdaq Composite adding about 0.9%.
The dollar started on the back foot after dropping to its lowest in more than three months against the yen overnight, as falling US Treasury yields made dollar-based investments less attractive.
On Monday, Dallas Federal Reserve President Richard Fisher and San Francisco Fed President John Williams both reinforced market expectations that the US central bank is in no hurry to hike interest rates.
Minutes of the Federal Reserve's last policy meeting are scheduled to be released on Wednesday, but are unlikely to give investors any solid clues about the timing of a US interest rate hike.
"Seven Federal Reserve Presidents are scheduled to speak around the release of the FOMC minutes and all of them will be just as elusive as Fed Chair Yellen in providing very little guidance on when rates will rise," said Kathy Lien, managing director of FX strategy for BK Asset Management.
"Aside from confirming their schedule for tapering, no additional outlook for monetary policy will be provided," she said in a note to clients.
The yield on benchmark US 10-year notes inched up to 2.54% in Asia from its US close of 2.53% on Monday, but remained close to six-month lows marked on Thursday last week.
That kept pressure on the greenback, with the dollar slightly down on the day at 101.47 yen, after dipping as low as 101.11 yen on Monday, its weakest level since early February.
The euro remained under pressure of its own, after European Central Bank officials signalled that further easing steps are likely to come next month.
The common currency was steady on the day at $1.3711, but remained not far from its low of $1.3648 hit on Thursday, which was its lowest since late February.
The Bank of Japan will conclude its latest policy meeting on Wednesday and is likely to maintain its upbeat view of the economy, suggesting no further easing steps are likely for the time being.
In commodities trading, US crude inched down slightly to $102.55 after the weaker dollar lifted it close to a one-month high in the previous session.