The announcement caused a dramatic turnaround in equity markets, which had retreated earlier under the combined impact of tensions in Hong Kong, economic crisis in Argentina, fears of a global slowdown -- and uncertainty over US-China trade talks.
But some of that uncertainty appeared to have lifted when the US said it was delaying until December 15 the imposition of new 10 percent tariffs on Chinese electronics.
Meanwhile, US Trade Representative Robert Lighthizer spoke with Chinese Vice Premier Liu He early Tuesday and has another call planned in two weeks, a USTR official told AFP.
- 'Ceasefire' -
===============
"US-China reach ceasefire on trade war," said Alfonso Esparza at OANDA.
"Equities surged with the news as the prolonged trade war has been the biggest negative factor hitting stocks," said Esparza.
US equities saw a dramatic turnaround after the news, with the tech-heavy Nasdaq index up around two percent, and the DJIA and S&P 500 indices not far behind.
Consumer electronics stocks led the way, with Apple more than four percent higher.
Oil prices, a bellwether for the global economic growth outlook, also surged, with Brent and WTI contracts up by around three percent.
Even though the US added that it was still going ahead with new duties starting September 1 on $300 billion in Chinese goods, it did not derail the markets' enthusiasm.
- Greenback surges -
====================
The dollar also firmed strongly, especially against the yen, euro and Swiss franc.
"The news of the delay of some US tariffs on certain Chinese goods is positive for risk sentiment, although the full details aren't yet known," said analysts at ING.
But "don't get carried away with optimism", they warned. "The lack of visibility on the trade war outlook means that the above should not translate into a long-lasting trend."
Until Trump rekindled hope on the trade war front, equities had been showing signs of buckling under what Lukman Otunuga at FXTM called "a burst of geopolitical risks across the globe".
Weakness in Asian stock markets had spilled first into Europe and from there into early US trading.
A big factor of worry was Hong Kong, where airport authorities on Tuesday suspended all check-ins as pro-democracy protesters blocked the facility.
- 'Economic populism is alive' -
================================
Emerging market currencies recovered from Monday's losses that came on the back of the shock win in an Argentina presidential primary election by populist centre-left candidate Alberto Fernandez over incumbent Mauricio Macri.
The news saw the country's peso dive 30 percent at one point and the stock market by even more.
OANDA Asia-Pacific senior market analyst Jeffrey Halley said "economic populism is alive and well in all corners of the globe -- a far more worrying development in the long-term than a US-China trade war".
Back in Europe, there was much concern at a surprisingly weak key survey out of Germany, by the ZEW institute, showing that confidence among investors hit its lowest ebb in almost eight years in August.
Analysts said a slowdown in powerhouse Germany would have repercussions across the eurozone.
- Key figures around 1450 GMT -
===============================
London - FTSE 100: UP 0.4 percent at 7,255.05 points
Frankfurt - DAX 30: UP 0.8 percent at 11,769.97
Paris - CAC 40: UP 1.3 percent at 5,375.54
EURO STOXX 50: UP 1.1 percent at 3,364.51
New York - Dow: UP 1.7 percent at 26,337.60
Hong Kong - Hang Seng: DOWN 2.1 percent at 25,281.30 (close)
Tokyo - Nikkei 225: DOWN 1.1 percent at 20,455.44 (close)
Shanghai - Composite: DOWN 0.6 percent at 2,797.26 (close)
Euro/dollar: DOWN at $1.1185 from $1.1217 at 2050 GMT
Pound/dollar: UP at $1.2072 from $1.2076
Euro/pound: DOWN at 92.65 pence from 92.84 pence
Dollar/yen: UP at 106.66 from 105.28 yen
Brent North Sea crude: UP $2.15 at $60.72 per barrel
West Texas Intermediate: UP $2.02 at $56.94