The yen eased slightly against the dollar in early currency deals in response to worse-than-expected Japanese industrial output figures that raise the possibility of further monetary easing by the country's central bank.
Tokyo jumped 0.90%, or 131.80 points, to 14,827.83, Sydney climbed 0.52%, or 27.9 points, to 5,394.8 and Seoul added 0.23%, or 4.61 points, to 1,985.61.
Hong Kong rose 0.39%, or 85.53 points, to finish at 22,151.06, but Shanghai slipped 0.41%, or 8.41 points, to 2,033.31.
Investors were unmoved by news that North and South Korea had traded live artillery fire across their disputed maritime border on Monday, forcing South Korean islanders to take shelter. The exchange came a day after the North drove up tensions by threatening a new nuclear test.
Regional investors took their lead from a positive finish to the week in the United States and Europe.
Wall Street rose after the Commerce Department said US consumer incomes and spending gained for a second straight month in February.
The Dow rose 0.36%, the S&P 500 added 0.46% and the Nasdaq gained 0.11%.
In Europe, London's FTSE 100, the CAC 40 in Paris and the DAX 30 in Frankfurt jumped after the European Commission said March consumer and business sentiment rose for the 11th month in a row, hitting a 30-month high.
Brad Gordon, investment adviser at Macquarie Equities in New Zealand, told Dow Jones Newswires that regional investors were given "a fairly positive lead from the US and European markets ... Friday".
In Japan on Monday, official data showed industrial output in February fell 2.3% month-on-month — the first fall in three months — following a 3.8% expansion in January.
Economists had widely predicted a 0.3% rise.
The data weighed on the yen as it could nudge the Bank of Japan towards widening its stimulus programme that was put in place last year to kickstart the economy.
The dollar fetched 102.96 yen against 102.80 yen in New York Friday, while the euro bought $1.3758 and 141.65 yen compared with $1.3752 and 141.38 yen.
Traders are awaiting the release on Tuesday of the Bank of Japan's Tankan survey of Japanese business sentiment, while the US Labor Department will on Friday unveil closely watched non-farm payrolls data for March.
On oil markets, New York's West Texas Intermediate for May delivery eased seven cents to $101.60 a barrel in early morning Asian trade, and Brent North Sea crude dipped 24 cents to $107.83.
Gold fetched $1,292 an ounce at 0800 GMT compared with $1,296.10 late Friday.
In other markets, Taipei rose 0.85%, or 74.64 points, to 8,849.28. Taiwan Semiconductor Manufacturing Co was 0.85% higher at T$118.5 while Uni-President Enterprise gained 1.92% to Tw$53.
Wellington was flat, edging down 2.91 points to 5,139.98.
Air New Zealand added 2.25% to NZ$2.04 while Fletcher Building was down 1.14% at NZ$9.52.
Manila closed 1.09% higher, adding 69.09 points to 6,428.71. Universal Robina rose 3.65% to 142 pesos, Ayala Land advanced 1.01% to 29.90 pesos and parent Ayala Corp gained 2.21% to 578 pesos.
Jakarta was closed for a public holiday.