World oil prices bobbed higher on concerns about tensions in the crude-rich Middle East, dealers said.
"Equities are attempting to claw back some lost ground," noted analyst Chris Beauchamp at trading firm IG, "but the overall atmosphere of caution still prevails".
On Wall Street the Dow had regained 320 points, or 1.3 percent, by the late morning, having lost a whopping 2.4 percent on Monday.
The tech-heavy Nasdaq, which had plunged 3.4 percent Monday, was also 1.3 percent higher at that time.
"US stocks are recovering from yesterday's drop in early action, which was the largest one-day fall since January, with the escalated trade tensions between the US and China continuing to be eyed," Charles Schwab analysts said.
They added, however, that President Donald Trump's statement that a meeting next month with Chinese President Xi Jinping would be "successful" gave investors some hope for a peaceful resolution of the trade standoff.
Europe's main stock markets were all higher at the close, with Paris the best performer.
- 'Bearish sentiment' -
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Earlier Tuesday Asian markets had plunged further in reaction to Monday's US stock plunge, seen after China hiked tariffs on $60 billion of US imports.
That has ramped up sizzling tensions in a trade war between the world's two biggest economic powers.
The latest move by Beijing was followed by a warning of further action such as dumping US Treasuries and came days after Washington more than doubled levies on $200 billion of Chinese goods and Trump said he was looking at more than $300 billion more.
"Ironically of course the tariffs imposed by both sides will hit consumers, so as in all great contests this is turning into a test of endurance, with the US and China each looking to derive the maximum impact from the increased charges in a bid to hit their opponent where it hurts," said Beauchamp.
The China-US trade conflict has sent shockwaves across trading floors, where most dealers had a little over a week ago been confident the two sides were close to a deal.
- Risk of volatility -
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After announcing the higher tariffs, the editor of the Communist Party-owned Chinese newspaper Global Times warned Beijing could also hit the US by offloading Treasuries, ending US agricultural purchases and reducing orders for Boeing airplanes.
However, while there is a lot of fear about an all-out trade war, which could batter the world economy, both said talks will continue, though no date has been set for the next round.
Also, Trump said he had a feeling talks with China will be "very successful" and that he intended to meet his Chinese counterpart at next month's G20 summit.
Elsewhere, oil prices advanced Tuesday as traders eyed Middle East woes, "sabotage attacks" on two Saudi Arabian oil tankers, and a growing crisis in Venezuela.
On Tuesday, drone attacks claimed by Iran-aligned Yemen rebels also shut down one of Saudi Arabia's main oil pipelines.
- Key figures around 1540 GMT -
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London - FTSE 100: UP 1.1 percent at 7,241.60 points (close)
Frankfurt - DAX 30: UP 1.0 percent at 11,991.62 (close)
Paris - CAC 40: UP 1.5 percent at 5,341.35 (close)
EURO STOXX 50: UP 1.3 percent at 3,364.38
New York - Dow: UP 1.3 percent at 25,648.43
Tokyo - Nikkei 225: DOWN 0.6 percent at 21,067.23 (close)
Hong Kong - Hang Seng: DOWN 1.5 percent at 28,122.02 (close)
Shanghai - Composite: DOWN 0.7 percent at 2,883.61 (close)
Euro/dollar: DOWN at $1.1210 from $1.1222 at 2100 GMT
Pound/dollar: DOWN at $1.2912 from $1.2958
Dollar/yen: UP at 109.65 yen from 109.30 yen
Oil - Brent Crude: UP 71 cents at $70.94 per barrel
Oil - West Texas Intermediate: UP 65 cents at $61.69 per barrel