The surge in U.S. stocks lifted MSCI's broadest index of Asia-Pacific shares outside Japan by 0.9%.
The Shanghai Composite Index advanced 0.6% while Hong Kong's Hang Seng, which has been hurt by disruptions from large anti-government protests, rose 0.5%.
South Korea's KOSPI advanced 0.8% and Japan's Nikkei rose 0.6%.
Yet Wednesday's bounce hardly clawed back the sizable losses for equities over recent months, and broad market sentiment remained fragile given that the U.S.-China trade conflict is still far from resolved.
Uncertainty around political risks such as the unrest in Hong Kong also continue to keep investors on edge.
Kenta Inoue, senior market economist at Mitsubishi UFJ Morgan Stanley Securities, pointed out that Trump's tariff delay came just as U.S. stocks were stalling.
"This appears to be a routine ploy by the U.S. president, who applies trade pressure on China when stocks are doing well and opts for compromise when they are not," Inoue said.
The S&P 500 advanced to a record high at the end of July, but it has lost momentum due to factors including U.S.-China trade angst. The index rose 1.5% on Tuesday, but is still down 1.8% in August.
The year-long tariff dispute between the world's biggest economies has already disrupted global supply chains and slowed economic growth.
Growth of China's industrial output slowed much more than expected to 4.8% in July from a year earlier, official data showed on Wednesday, in the latest sign of faltering demand as the United States ramps up trade pressure. July's pace was the slowest since February 2002.
"President Trump did delay the tariffs and while this is positive for equities, the markets will remain wary of the tariffs still being implemented come December," said Masahiro Ichikawa, senior strategist at Sumitomo Mitsui DS Asset Management.
"And while the tensions in Hong Kong are not a main calibre theme for all markets, their negative impact has been multiplied as they have taken place simultaneously with developments in Argentina."
Fears of a possible return to interventionist policies, and by extension a possible debt default, jolted global markets this week after conservative Argentina President Mauricio Macri was handed a trouncing by the opposition in presidential primaries over the weekend.
In currencies, the safe-haven yen advanced 0.45% to 106.260 per dollar as market participants took a sceptical view of Trump's decision to delay tariffs on some Chinese goods.
In volatile trading, the yen retreated to 106.980 per dollar overnight before finding its footing. On Monday, the Japanese currency had brushed a seven-month peak near 105.000.
The dollar index versus a basket of six major currencies inched down 0.05% to 97.759 after advancing nearly 0.5% the previous day.
The euro was steady at $1.1175 after slipping 0.4% against the dollar on Tuesday.
The greenback's advance stalled as the sharp rise in U.S. yields seen overnight ran out of momentum.
The 10-year U.S. Treasury note edged down 2.5 basis points to 1.676% after climbing 6 basis points overnight. The yield had plumbed a three-year low of 1.595% a week ago.
Brent crude oil futures were down 0.83% at $60.79 per barrel, losing steam after soaring nearly 5% the previous day.
Crude prices jumped on Tuesday as Washington's decision to delay imposing some tariffs eased worries about a global economic slowdown, at least for the time being.
(Editing by Shri Navaratnam and Richard Borsuk) ((firstname.lastname@example.org; +813-6441-1774))