US President Donald Trump said he had an "extraordinary" relationship with Chinese President Xi Jinping and trade talks had not yet collapsed. Earlier in the day, China said it agreed to continue talks on trade.
The pan-European STOXX 600 index climbed 1%, lifting off Monday's two-month low which came after China slapped retaliatory tariffs on US goods, spurring investors into scaling back risky bets as they fled to safer shores.
Robert Griffiths, equity strategist at Credit Suisse, said he believed Trump would not be willing to risk the effect a second round of tariffs would have on the US economy, thus leaving scope for a de-escalation.
Germany's trade-sensitive DAX and London-listed equities tacked on 1%, while French stocks gained 1.5%.
Trade sensitive European auto and tech stocks bounced 2.2% and 1.2% each, after being caught at the heart of Monday's selloff, at which point the STOXX 600 had outperformed the S&P 500.
Lukas Daalder, BlackRock's chief investment strategist for the Netherlands, said hopes the euro zone economy is through the worst and bottoming out, relatively low valuations and optimism around a US-China deal will soon be brokered were helping fuel the gains.
However, the STOXX 600 is down 3.8% this month, set for its biggest monthly loss since December.
Among auto stocks, Ferrari added 3.3%, leading the sector index's rise. On the other hand, Renault tempered sector gains, falling 2.3%.
The French carmaker's Japanese partner, Nissan Motor Co , flagged its weakest annual profit in more than a decade.
Banks rose 0.9% percent, with Commerzbank up 4.3% after Reuters reported UniCredit had stepped up preparations for a potential bid for the German lender.
Unicredit shares fell 1.7%, on a day when Italian banks' shares were pressured due to their holdings of the country's sovereign bonds.
Italian cable maker Prysmian and German pharma group Evotec climbed 7.5% and 5%, respectively, on positive earnings updates.
Vodafone slid after a dividend cut, walking back on a pledge to maintain one of the biggest payouts in Britain, so it can build 5G networks and complete its looming acquisition of Liberty Global assets.
Bayer shares ended 2% lower, after hitting seven-year lows earlier in the day. A jury awarded more than $2 billion to a California couple in the largest US jury verdict against the company over allegations its Roundup weed killer causes cancer.