A wave of optimism flowed across stock markets on Tuesday, building on Wall Street's gains the previous session, as fears of a US-China trade war receded.

Speculation that Kim Jong Un paid a surprise secret visit to Beijing also lifted spirits -- and the South Korean won -- as the North Korean leader prepares for possible nuclear talks with US President Donald Trump.

In Europe, takeover activity boosted sentiment -- with shares in GlaxoSmithKline jumping six percent after the British drugs giant agreed to buy Novartis' stake in the pair's consumer healthcare joint venture for $13 billion.

The Swiss group said the sale of the 36.5-percent stake would enable it to focus on its core pharmaceutical business. Novartis shares rose 2.3 percent.

"European markets are in rebound mode, with yesterday's relief rally in the US helping drive gains across Asia and Europe," noted Joshua Mahony, market analyst at IG trading group.

"Yesterday's 664-point rally in the Dow amounted to the third biggest single day point gain in history, with investors beginning to see light at the end of the tunnel after a period which threatened to see a global trade war break out."

Around 1030 GMT, London's benchmark FTSE 100 index was up 1.9 percent compared with Monday's close.

In the eurozone, Frankfurt's DAX 30 index rallied 2.0 percent and the Paris CAC 40 advanced 1.5 percent.

The euro dropped against the dollar, which rose also versus the pound and yen.

Meanwhile, gains across stock markets chipped away at the sharp losses suffered last week in response to the White House's decision to hit China with billions of dollars in tariffs.

That came weeks after Washington announced levies on steel and aluminium imports that sparked talk of a trade war that could batter the global outlook, but those tariffs have since been postponed for some countries.

However, nerves have been soothed this week as it emerged that high-level talks had been taking place between the world's top two economies to find an agreement.

US markets surged Monday, with the Dow and S&P 500 almost three percent higher and the Nasdaq piling on 3.3 percent -- its biggest one-day rise since August 2015.

Those strong performances continued in Asia, with Tokyo closing 2.65-percent higher on Tuesday, thanks to a drop in the yen against the dollar, as traders shift out of assets considered safe in times of uncertainty and turmoil.

Seoul rose 0.6 percent and the won climbed more than one percent against the dollar on speculation Kim had visited China -- in what would have been his first trip outside North Korea since assuming power at the end of 2011.

And if confirmed, the visit would mark the latest development in the fast-paced shift towards an easing of tensions on the Korean peninsula.

Elsewhere Tuesday, Shanghai's main stocks index ended up 1.1 percent.  (AFP)