White House adviser Larry Kudlow said tariffs scheduled for December could be withdrawn if talks go well, adding to optimism after China said it would work with the United States to address each other's core concerns.
In Britain, the parliament's speaker refused to allow a vote on Boris Johnson's divorce deal with the European Union, suggesting the British prime minister faces further problems in Brexit ratification.
Johnson's opponents in parliament on Saturday demanded a change to the sequencing of the ratification of the deal, forcing him to request a delay.
MSCI's world equity index, which tracks shares in 47 countries, gained 0.6pc. The Euro STOXX 600 added 0.6pc, while the S&P 500 index was also up 0.6pc.
"It looks like the global economy has settled and worries that we're falling into the depths of a recession have eased," said Alan Lancz, president of Alan B. Lancz & Associates Inc., an investment advisory firm based in Toledo, Ohio.
"It's a more settled market," he said. Also, "it's a matter of maybe things just on hold politically."
On Friday, Chinese Vice Premier Liu He said that Beijing will collaborate with the United States to address mutual concerns on the trade war.
Stocks investors are also gearing up for more high-profile earnings reports this week from such companies as Microsoft Corp and Amazon.com Inc..
On Wall Street, the Dow Jones Industrial Average rose 50.61 points, or 0.19pc, to 26,820.81, the S&P 500 gained 19.97 points, or 0.67pc, to 3,006.17 and the Nasdaq Composite added 70.69 points, or 0.87pc, to 8,160.23.
The dollar index was up 0.1pc in afternoon trading, while sterling was last trading at $1.2963, down 0.06pc on the day.
The Chilean peso was down about 2pc and on track for its biggest daily percentage decline in more than six years after a state of emergency was declared in the capital city of Santiago following violent protests over the weekend.
Against the dollar, sterling was last up 0.1pc in North American trade, having earlier broken above $1.30 for the first time in 5-1/2 months. The euro was 0.18pc higher against the dollar, having also been lifted by Brexit optimism this month by 2.23pc.
In the US bond market, benchmark 10-year notes last fell 11/32 in price to yield 1.787pc, from 1.75pc late on Friday.
In commodities, oil prices fell. US crude fell 0.9pc to settle at $53.31 per barrel and Brent settled at $58.96, down 0.8pc on the day.