The dollar was mixed against main rivals, while the pound won support from official data showing UK unemployment held at a 45-year low point with a rate of 3.8 percent.

"Safe to say, the changing expectations for interest rates is the primary reason for such a strong rebound in the (stock) markets that didn't look particularly likely at the start of last week," said Oanda senior market analyst Craig Erlam.

"Once again, it's central banks that are left to fill the economic void, easing investor fears over trade wars and a global slowdown."

Friday's weak US jobs report has increased expectations that the Federal Reserve will look to cut interest rates, weighing on the dollar but boosting stock markets around the world.

Brexit uncertainty has meanwhile reduced expectations of a rate hike from the Bank of England any time soon, while the European Central Bank has vowed support to stimulate a struggling eurozone economy.

Rising prospects of a US rate cut come as President Donald Trump has threatened new tariffs against Beijing amid an escalating trade war.

China on Tuesday did not confirm a planned face-to-face meeting between President Xi Jinping and Trump.

Trump said a meeting with Xi has been "scheduled" during the G20 summit in Japan later this month, and that he expected the Chinese leader to attend.

A Trump-Xi meeting would mark a turning point in the bruising trade dispute between the world's two biggest economies that has spooked markets worldwide and sparked worries about the global economy.

At the same time, Trump's decision to drop threatened tariffs on Mexico sparked relief across trading floors and led to hope that the row with Beijing could also end with some sort of agreement.

Tuesday's stock market gains, which follow another healthy Wall Street performance Monday, are much needed since the US president shocked markets last month by hiking levies on $200 billion of Chinese imports, blaming backsliding over their long-running trade talks.

Elsewhere on Tuesday, oil prices recovered slightly having dropped Monday on uncertainties about an agreement between crude producing nations to cap output.

- Key figures around 1045 GMT -

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London - FTSE 100: UP 0.5 percent at 7,410.02 points

Frankfurt - DAX 30: UP 1.3 percent at 12,198.44

Paris - CAC 40: UP 0.8 percent at 5,423.68

EURO STOXX 50: UP 0.8 percent at 3,412.98

Tokyo - Nikkei 225: UP 0.3 percent at 21,204.28 (close)

Hong Kong - Hang Seng: Up 0.8 percent at 27,789.34 (close)

Shanghai - Composite: UP 2.6 percent at 2,925.72 (close)

New York - Dow: UP 0.3 percent at 26,062.68 (close)

Euro/dollar: UP at $1.1319 from $1.1316 at 2040 GMT Friday

Pound/dollar: UP at $1.2719 from $1.2686

Dollar/yen: UP at 108.69 yen from 108.49 yen

Oil - Brent North Sea: UP 23 cents at $62.52 per barrel

Oil - West Texas Intermediate: UP 46 cents at $53.72 per barrel