Britain's FTSE100 index was up 0.7%, Germany's DAX rose 0.5%, and France's CAC40 index was up 0.6%.
A Chinese state-backed tabloid said on Monday China and the United States were "very close" to an initial trade agreement, adding to optimism from Friday, when the presidents of both the countries reiterated their desire for a deal.
China said on Sunday it would seek to improve protections for intellectual property rights, including raising the upper limits for compensation for rights infringements.
"China being prepared to look at intellectual property is obviously the catalyst for a nice move higher, or a return to the highs earlier this month," said Michael Hewson, chief markets analyst at CMC Markets in London.
Earlier in Asia, MSCI's broadest index of Asia-Pacific shares outside Japan bounced 0.7%, after losing 0.4% last week.
Japan's Nikkei firmed 0.7%, while Australian stocks rose 0.5% and Shanghai blue chips 0.3%.
E-Mini futures for the S&P 500 added 0.2%.
On Saturday, U.S. national security adviser Robert O'Brien said an initial trade agreement with China is still possible by the end of the year, though he warned Washington would not turn a blind eye to what happens in Hong Kong.
The comments add to worries that a Chinese crackdown on anti-government protests in Hong Kong could further complicate the talks.
"The fact that talks are still happening remains a positive," said Robert Rennie, head of financial market strategy at Westpac. "Markets are showing some signs of tiring of the steady drip feed of upbeat comments from U.S. officials and no signs of a final agreement looking likely."
He said seeks had passed since the "phase one" deal was agreed in principle yet there was still no deal in place.
"Key for markets will thus be whether the Dec. 15 tariffs covering approximately $156 billion of largely technology imports are postponed and whether a deal can be signed ahead of that date, with press suggesting that these tariffs will be delayed to give negotiators more time."
In currency markets, the dollar dipped after its rally on Friday when U.S. manufacturing surveys beat forecasts, just as European Union numbers disappointed.
Against a basket of currencies, it last traded down 0.05% at 98.226, after gaining 0.3% last week.
"U.S. economic data outperformed, highlighting again the resilience of the economy and that while global growth has slowed, it remains the least dirty t-shirt in the laundry basket," said Tapas Strickland, a director of economics and markets at National Australia Bank.
"For the EU data, the important takeaway was the ongoing decline in the manufacturing sector is now spreading to the larger services sector, a worrying sign for the global economy."
European Central Bank President Christine Lagarde on Friday called on euro zone governments to strengthen domestic demand.
Federal Reserve Chair Jerome Powell speaks later on Monday and is expected to underline the steady outlook for rates given the better economic figures.
The euro was flat $1.1024 on Monday, having breached chart support at $1.1040, while the dollar edged up to 108.87 yen.
Spot gold was 0.3% lower at $1,457.44 per ounce.
Oil prices rose.
Brent crude futures firmed 0.19% to $63.51, while U.S. crude rose 0.1% to $57.83 a barrel.
(Reporting by Ritvik Carvalho; additional reporting by Wayne Cole in Sydney, Editing by Angus MacSwan) ((Ritvik.Carvalho@thomsonreuters.com; +44 2075429406; Reuters Messaging: email@example.com))