Optimism that central banks will provide fresh support to head off a global economic recession has also lent much-needed support to regional equities after last week's sell-off, with eyes on an upcoming speech by Federal Reserve boss Jerome Powell for clues about its plans.
Investors were in an upbeat mood after White House chief economic adviser Larry Kudlow said that if talks between deputies from Beijing and Washington went well and "we can have a substantive renewal of negotiations" then "we are planning to have China come to the USA and meet with our principals to continue the negotiations".
He added that high-level phone talks last week were "a lot more positive than has been reported".
Trump provided further cause for hope by tweeting: "We are doing very well with China, and talking!"
Kudlow also raised the prospect of using cash taken from higher tariffs on Chinese goods to pay for tax cuts.
"This sort of recycling won't clear the oceans of plastic or reduce global warming, but it is an elegant solution to reducing the pain of tariffs on the American consumer of China and may give equity markets a small boost as we start the week," said Jeffrey Halley, senior market analyst for Asia-Pacific at OANDA.
- US recession warning -
The remarks helped Asian traders build on New York's rally. Hong Kong led gainers, surging more than two percent in the afternoon with dealers also cheered by three days of protests in the city passing off peacefully. Shanghai ended up 2.1 percent and Tokyo added 0.7 percent.
Sydney climbed one percent, Singapore put on 0.6 percent and Seoul jumped 0.7 percent with Wellington, Taipei and Jakarta deep in positive territory.
In early trade London gained 0.8 percent, Frankfurt put on one percent and Paris jumped 0.9 percent.
There remains a high level of concern about the global outlook and particularly the US economy after yields on 10-year US Treasury bonds slid last week below that of the two-year note, while the 30-year yield fell below two percent for the first time ever.
The so-called "inversion" -- when short-term interest rates are higher than longer-term ones -- is viewed as a harbinger of recession.
Investors are hopeful that authorities will unveil stimulus to limit any impact. Germany's Der Spiegel said Angela Merkel's government was ready to boost public spending, while China announced an interest rate reform that it said would lower borrowing costs for companies.
But the US is forecast to fall into recession in the next two years, according to a survey released Monday by the National Association for Business Economists.
The economists are also sceptical about a resolution to Trump's trade wars, although 64 percent said a "superficial agreement is possible", NABE said.
The report came just after Trump pushed back against recession talk, saying: "I don't think we're having a recession. We're doing tremendously well. Our consumers are rich."
"I gave a tremendous tax cut, and they're loaded up with money. They're buying. And most economists actually say that we're not going to have a recession. But the rest of the world is not doing well like we're doing."
And Kudlow insisted that the outlook was far from gloomy. "Let's not be afraid of optimism," he said, adding that "I sure don't see a recession."
On oil markets, both main contracts jumped more than one percent on trade hopes and after a drone attack by Yemeni rebels on a Saudi Arabian field over the weekend.