Uncertainty remained high, however, about the next developments in the trade dispute, which has repeatedly seen the sides attempt to negotiate before ending in acrimony and more tariffs and trade penalties.
After Asian shares mostly fell on concerns about an escalation Friday in the dispute, markets in Europe and U.S. futures perked up after Trump said that his trade negotiators had received two "very good calls" from China on Sunday. China's foreign ministry replied, however, that it didn't know what Trump was talking about.
France's CAC 40 was up 0.6% to 5,360, while Germany's DAX rose 0.5% to 11,665. Markets were closed in Britain for a national holiday. U.S. shares were set to recover, with Dow futures up 0.6% and S&P 500 futures up nearly 0.5%.
The Dow Jones Industrial Average plunged more than 600 points on Friday and the S&P 500 suffered its fourth straight weekly loss after Trump responded angrily on Twitter following China's announcement of new tariffs on $75 billion in U.S. goods. In one of his tweets he "hereby ordered" U.S. companies with operations in China to consider moving them to other countries - including the U.S.
Trump also later announced that the U.S. would increase existing tariffs on $250 billion in Chinese goods to 30% from 25%, and that new tariffs on another $300 billion of imports would be 15% instead of 10%.
Stephen Innes, managing partner at Valour Markets in Singapore, compared the difficulty of assessing the volatile market situation to reading tea leaves.
"Nobody understands where the president is coming from," he said, adding that the best thing Trump can do for market stability is to "keep quiet."
"The problem that we're faced right now is that we are making a lot of assumptions ahead of the economic realities," he said.
The market is now dominated by fears of a portending U.S. recession, although the American economy is actually holding up, and much of the U.S. economy is made up of consumption, Innes said. If interest rates come down, he added, consumer spending is likely to go up, working as a buffer for the economy.
"What the market's really waiting for is for (the U.S. Federal Reserve) to drop interest rates," Innes said. "Right now, we are still sitting on that uncertainty."
Some analysts think the Fed will lower interest rates again this year. Fed Chair Jerome Powell indicated last week that the central bank was prepared to cut interest rates but gave no clear signal on when or by how much, while suggesting that uncertainty over Trump's trade wars have complicated the central bank's ability to set interest rate policy.
A quarter-point rate cut reduction in September is considered all but certain. Some think the Fed will cut rates again in December.
Meanwhile, China allowed its currency, the yuan, to fall further on Monday. That effectively helps its exporters, negating some of the effects of higher U.S. tariffs.
The yuan declined to 7.1468 to the dollar, a relatively modest change from Friday's low point of 7.0927 but its weakest rate since January 2008. The yuan has lost 6.5% from this year's high on Feb. 28. Chinese leaders have promised to avoid "competitive devaluation" to hold down export prices in the face of Trump's tariff hikes.
Japan's benchmark Nikkei 225 started plummeting as soon as trading began and finished at 20,261.04, down 2.2%. Australia's S&P/ASX 200 slipped 1.3% to 6,440.10. South Korea's Kospi lost 1.6% to 1,916.31. Hong Kong's Hang Seng dropped 1.9% to 25,680.33, while the Shanghai Composite was down 1.2% at 2,863.57.
Economists say that the unpredictability of the trade dispute is at least as damaging as the tariffs themselves, affecting the decisions of central banks and companies as they plan investments.
Zhu Huani, analyst at Mizuho Bank in Singapore, said that what he called Trump's "tariff tantrum" was setting off "the sense that tariffs could continue to rise," with the "the unpredictability of timing and extent of these trade actions risk accentuating the paralysis of business decisions and big-ticket business spending."
"No matter which way you cut the cake, it is nearly impossible to construct a bullish, or even neutral scenario for equity markets today," said Jeffrey Halley, senior market analyst at Oanda.
The price of benchmark crude gained 54 cents to $54.71 a barrel. It sank $1.18, or 2.1%, to settle at $54.17 a barrel Friday, as traders worried that the latest escalation in the trade battle could sap global demand for energy. Brent crude oil, the international standard, rose 42 cents to $59.76 a barrel.
The dollar fell to 105.88 Japanese yen from 106.65 yen on Friday. The euro strengthened to $1.1118 from $1.1057.
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