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Shrugging off last week's losing streak, Asian markets also ended higher.
Wall Street initially followed their lead as a new round of high-stakes talks got underway to resolve the festering trade row, but then ran into profit-taking by the late New York morning.
US traders reported edginess in the market as uncertainty over congressional budget talks sparked talk of another possible government shutdown.
US negotiators meanwhile met their Chinese counterparts for preliminary discussions in Beijing on Monday, buoying hopes of a deal.
"European stocks have rallied ... as traders are hopeful about the next round of trade talks between the US and China," said CMC Markets analyst David Madden.
"Given that both sides are still far apart, there is no guarantee that the discussions will be successful, and dealers' optimism might be wishful thinking."
London's benchmark FTSE 100 rose after an announcement that UK economic growth has slowed weighed on the pound, lifting stocks in multinationals that have earnings in foreign currency.
With Brexit looming next month, the British economy grew by 1.4 per cent last year, data showed. That was the lowest level for six years, and down from 1.8 per cent in 2017.
But Asian equities experienced sizeable gains on Monday on resurgent investor optimism.
"It's shaping up to be another big week for the United States, with the government on the verge of another shutdown and trade talks continuing with China," said Oanda analyst Craig Erlam.
Mainland Chinese markets rebounded on Monday after the Lunar New Year break despite a bleak IMF warning over the global growth outlook.
Top US economic officials will travel to the Chinese capital this week for the third round of talks on Thursday and Friday, but deputies had already arrived and the White House said preparatory discussions were to begin Monday.
Failure to agree a deal between the two economic superpowers before Mar 1 would see punitive US duties on US$200 billion in Chinese goods more than double.
Analysts say imposition of the tariffs could further sap the strength of the global economy.
Over the weekend, the International Monetary Fund warned governments to prepare for a possible global economic "storm" as growth forecasts dip.
It cited the trade row as one of four "clouds" overshadowing the global economy, along with Brexit uncertainty, the accelerated slowdown in China, and financial tightening.
"The bottom-line - we see an economy that is growing more slowly than we had anticipated," IMF chief Christine Lagarde said.
Looming later this week is the spectre of a repeat of the 35-day partial US government shutdown that ended Jan 25 - the longest in the country's history.
Key figures around 1635 GMT:
London - FTSE 100: UP 0.8 per cent at 7,129.11 points (close)
Frankfurt - DAX 30: UP 1.0 per cent at 11,014.59 (close)
Paris - CAC 40: UP 1.1 per cent at 5,014.47 (close)
EURO STOXX 50: UP 1.0 per cent at 3,167.36
New York - Dow: DOWN 0.1 per cent at 25,088.50
Hong Kong - Hang Seng: UP 0.7 per cent at 28,143.84 (close)
Shanghai - Composite: UP 1.4 per cent at 2,653.90 (close)
Tokyo - Nikkei 225: Closed for a public holiday
Euro/dollar: DOWN at US$1.1281 from US$1.1323
Dollar/yen: UP at 110.37 yen from 109.73
Pound/dollar: DOWN at US$1.2863 from US$1.2944 at 2200 GMT Friday
Euro/pound: UP at 87.69 pence from 87.40 pence
Oil - Brent Crude: DOWN 93 cents at US$61.17 per barrel
Oil - West Texas Intermediate: DOWN US$1.23 cents at US$51.49 per barrel