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Investors are hoping Beijing and Washington will avoid another escalation in tariffs like the one that occurred after talks collapsed in May.
Officials have downplayed the potential for a breakthrough, however, since the same issues that caused talks to bog down earlier remain.
Treasury Secretary Steven Mnuchin and Trade Representative Robert Lighthizer will meet on Tuesday and Wednesday in Shanghai with a delegation led by China's economy czar, Vice Premier Liu He.
A working dinner is reportedly scheduled for later with talks scheduled for Wednesday.
The talks resume amid an array of disputes that has grown to include tension over Chinese tech giant Huawei.
Presidnt Trump in a series of tweets said that negotiations with China could get tougher.
Presidents Donald Trump and Xi Jinping agreed in June to revive efforts to end the costly fight over China's technology ambitions and trade surplus.
Trump has repeated his claim that the United States is prospering by "taking in tens of billions of dollars" from his tariff hikes on Chinese products. In reality, those are paid by U.S. companies and often trickle down to consumers who buy Chinese goods.
Chinese leaders are resisting U.S. pressure to roll back plans for government-led development of industry leaders in robotics, artificial intelligence and other technologies.
Washington complains those efforts depend on stealing or pressuring foreign companies to hand over technology.
The June agreement to resume negotiations helped to calm jittery financial markets despite warnings by economists that with both sides still far apart on critical issues, the fragile truce likely will soon fall apart.
Tensions worsened when, after talks broke down in May, the Trump administration imposed curbs on U.S. technology sales to Huawei, the biggest global maker of network gear for phone companies and the No. 2 smartphone brand. U.S. officials view Huawei as a national security threat and warn that its equipment could be used for cyberespionage.
"The only problem with these deals is the have internal, domestic politics to deal with," Laffer told FOX Business. "China has domestic industries to deal with that are tough, and so [does the U.S.]. The steel industry doesn't want a great deal. There are a lot of industries that don't want it. It's tough to make it happen."
The tariff hikes are battering exporters on both sides and disrupting trade in goods from soybeans to medical devices.
China's imports of American goods fell 31.4 percent in June from a year ago while exports to the United States fell 7.8 percent.
China agreed earlier to narrow its multibillion-dollar trade surplus with the United States by purchasing more American soybeans, natural gas and other exports. But it revoked that pledge after one of Trump's tariff hikes last year.
"Both countries want a good deal," Laffer told FOX Business. "It's a win-win for everyone in the world."
FOX Business' Blair Shiff and the Associated Press contributed to this article.