Japan's shares rose despite a central bank survey showing firms expect inflation to rise 1.4% a year from now, casting doubts on the bank's pledge to hit 2% this fiscal year.
The Nikkei 225 ended up 1.5% at 19,312.79, leading the region's gains.
That is its biggest daily percentage gain since 12 February.
Investors are also awaiting key jobs figures from the US on Friday.
Concerns over the health of the world's largest economy were raised after data on Wednesday showed the pace of US manufacturing growth in March eased to its slowest in nearly two years.
The dollar remained under pressure, buying 119.62 yen.
In China, the Shanghai Composite closed 0.4% higher at 3,825.78, while Hong Kong's Hang Seng index ended up 0.8% at 25,275.64.
In Australia, the S&P/ASX 200 closed up 0.7% at 5,898.6 as bank stocks were boosted on growing expectations of an interest rate cut by the central bank next week.
A private survey also showed that inflation rose from a five-year trough in March as petrol prices rebounded.
The TD Securities-Melbourne Institute's monthly measure of consumer prices rose 0.4% in March, from February when it had been unchanged.
The annual pace was up to 1.5%, from 1.3%, but stayed well below the central bank's target band of 2% to 3%.
The Australian market will be closed on Friday and Monday for the Easter holiday.
South Korean shares closed flat after data showed the country's seasonally-adjusted current account surplus in February at a record high for the second consecutive month.
Exports in February rose by 2% from January while imports fell 0.4%.
The benchmark Kospi index was at 2,029.07.
Asian shares rose on Thursday despite investors being cautious ahead of a Good Friday public holiday in some major markets.