Investors were given a healthy lead from Europe where London and Frankfurt ended at record highs but below-par Chinese figures tempered gains.
Hong Kong rose 0.4 percent to levels not seen since mid-2015, while Shanghai put on 0.3 percent, putting it on track for a third straight win, having tumbled about seven percent since April on worries about a government crackdown on leveraged investment.
Seoul added 0.2 percent as investors ignored another missile test by North Korea at the weekend, while Singapore climbed 0.5 percent.
However Tokyo ended the morning 0.2 percent lower on the back of a stronger yen. Sydney was flat.
In China, official data showed output from the country's factories and workshops slowed more sharply than expected in April, while retail sales were also below par.
The data comes as China hosts an international summit showcasing its Silk Road project that it hopes will revive ancient trading routes and breathe life into the world's number two economy, which grew last year at its slowest pace in a quarter of a century.
On Wall Street the Dow ended in the red after another weak set of results from top stores JC Penney and Nordstrom, which added to concerns about the world's biggest economy's key retail sector. The downbeat came a day after disappointing earnings from Macy's.
Adding to the sense of worry were US retail sales and inflation data that fell short of expectations and had investors rethinking expectations for the Federal Reserve's rate of interest rate hikes this year.
Stephen Innes, senior trader at OANDA, said in a note that the readings "did little to convince investors that a recent run of weak US economic performance was reversing".
"If the deterioration in tier one US economic data continues, I think it will be time for a reality check" regarding the Fed's rate plans.
