• Stocks closed higher after a choppy session on Tuesday as comments from President Donald Trump's top economic advisor sparked some hope the U.S. and China will strike a compromise on trade.

The Dow Jones Industrial Average rose 108.49 points to 24,748.73, while the S&P 500 gained 0.3 percent to end the day at 2,682.20. The Nasdaq Composite just above the flatline at 7,082.70. At its low of the day, the Dow dropped more than 200 points.

• The indexes rose after National Economic Council Director Larry Kudlow said the White House was having "a lot of communication with the Chinese government at all levels" ahead of a meeting between Trump and his Chinese counterpart, Xi Jinping. Kudlow later told reporters Trump thinks there is a "good possibility" the two countries can reach and agreement.

• "The whole year comes down to the next few weeks," said Brent Schutte, chief investment strategist for Northwestern Mutual Wealth Management. "Most of what's happening is geopolitics-related. If we can get clarity on any of those things (tariffs, Brexit, the Italian budget), especially tariffs, that would be positive for the market."

• Kudlow's comments came after Trump told The Wall Street Journal that it was "highly unlikely" that the U.S. would delay from increasing tariffs on $200 billion in Chinese goods to 25 percent. Trump went onto suggest that a 10 percent tariff on laptops and iPhones imported from China could be imposed.

• European stocks dropped on Tuesday afternoon, as investors monitored a number of political events including Brexit and Italian budget plans, and digested further comments from President Donald Trump.

The pan-European Stoxx 600 provisionally closed 0.2 percent lower with the various sectors taking different directions. Autos and Basic Resources were the worst-performing sectors, on the back of ongoing trade concerns.