About 40 minutes into trade, the Dow Jones Industrial Average was up 176.91 points (1.09 per cent) at 16,462.42.
The broad-based S&P 500 gained 23.76 (1.22 per cent) at 1,964.27, while the tech-rich Nasdaq Composite Index advanced 61.83 (1.32 per cent) to 4,759.37.
The gains in the US extended yesterday's big rally, which snapped a six-day losing streak.
Earlier today, the Shanghai market, whose plummet unleashed the global sell-off of the last 10 days, soared 5.34 per cent. Exchanges in London, Frankfurt and Paris were up around three per cent.
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All 30 members of the Dow rose, with oil producers Chevron (+2.9 per cent) and ExxonMobil (+2.2 per cent) among the bigger gainers.
Other petroleum-linked stocks also surged on higher oil prices. Driller Nabors Industries jumped 7.4 per cent, EOG Resources gained 4.9 per cent and ConocoPhillips added 4.2 per cent.
High-flying technology stocks also prospered, including Facebook (+2.4 per cent), Netflix (+5.6 per cent) and Tesla Motors (+5.7 per cent).
Metals and oil producer Freeport-McMoRan powered 18.3 per cent higher as it announced deep cuts to its capital budget in light of weak commodity prices. Freeport now expects to spend USD 4 billion in 2016, down 29 per cent from its estimate a month ago.
PVH, which owns the Tommy Hilfiger and Calvin Klein apparel brands, rose 4.5 per cent as it lifted its full-year profit forecast to USD 6.90-USD 7.00 per share, five cents above the prior range.
Bond prices were mixed. The yield on the 10-year US Treasury rose to 2.20 per cent from 2.18 per cent yesterday, while the 30-year held steady at 2.94 per cent. Bond prices and yields move inversely.