Japan's Nikkei rose 1.0% to hit a two-month high while MSCI's broadest index of Asia-Pacific shares outside Japan was flat, not far from a one-year high hit last week.
Asian shares were bolstered by the US Institute for Supply Management's manufacturing activity index May rising to 55.4 in May from 54.9 in April.
The data initially caused some confusion in US trade because the ISM initially announced a far weaker 53.2 and took nearly three hours to issue a correction.
In the end, though, the corrected figure was nearly in line with expectations. Coupled with other data showing a rise in construction spending, it suggested a healthy recovery after the first quarter's weather-related contraction.
The data followed a gauge of China's factory activity showing expansion at the fastest pace in five months in May, helping to lift MSCI's world index to a 6-1/2-year intraday high about 1.5% away from its lifetime record set in late 2007.
"On the whole, the world's economy is looking up, growing at a moderate pace," said Ayako Sera, senior market economist at Sumitomo Mitsui Trust Bank.
As solid gains in equity prices undermined the allure of safe-haven assets, gold flirted with a four-month low of $1,240.65 an ounce hit on Monday, having fallen for five days in a row. It last traded at $1,244.79.
Silver also stood near a one-year low of $18.60 hit on Friday, changing hands at $18.74.
The yield on the 10-year US Treasuries posted the largest daily advance in more than six weeks on Monday, jumping back to 2.53% compared to an 11-month low of 2.40% hit on Thursday.
Global bond yields had fallen sharply in the past few weeks partly on expectations that the European Central Bank will adopt a series of easing measures at its meeting on June 5.
Such expectations have driven the euro down, and the common currency stood at $1.3596, just a hair above its 3 1/2-month low of $1.3586 hit on Thursday.
In contrast, the dollar index rose to its highest level since Feb. 13 at 80.681, and last stood at 80.631, helped by the solid US data.
Against the yen, the dollar rose to 102.49 yen overnight, its highest in a month, though the currency is still stuck in a familiar range.
The dollar's resurgence put some emerging market currencies under pressure.
The Brazilian real fell to a two-month low of 2.2770 to the dollar also due to the worsening economic outlook in the biggest economy in South America and uncertainty on the central bank's currency intervention programme.
The South African rand also hit a two-month low of 10.6960 to the dollar on Monday, hurt by a recent raft of weak data. In Asia the Indonesian rupiah hit a three-month low of 11,785 to the dollar on an unexpected trade deficit in April.
In Asia, the Australian and Indian central banks hold policy meetings later in the day, though neither of them is expected to change its policy rate.