Stocks rose on Thursday on the back of a report that said the U.S. could ease tariffs on Chinese goods during their trade negotiations with China.

That idea was floated by Treasury Secretary Steven Mnuchin, according to a Wall Street Journal report, which cited people close to the matter. The report, however, added that Mnuchin faced pushback from U.S. Trade Representative Robert Lighthizer, who thinks any concession could be seen as a sign of weakness.

The report sent stocks to their highs of the day, with the Dow Jones Industrial Average rising more than 250 points. The and Nasdaq Composite both rose about 1 percent following the report.

However, the major indexes came off their highs after a Treasury Department spokesperson working with the trade team told CNBC: "Neither Secretary Mnuchin nor Ambassador Lighthizer have made any recommendations to anyone with respect to tariffs or other parts of the negotiation with China. This is an ongoing process with the Chinese that is nowhere near completion."

A senior administration official who participated in a trade meeting with the president on Wednesday later told CNBC that there is "no discussion of lifting tariffs now." The official also said President Donald Trump "has no interest in making decisions now, it would put him in a weaker position."

The Dow closed up 163 points, lifting itself out of correction territory. The S&P 500 ended the day up 0.76 percent while the Nasdaq climbed 0.7 percent.

"The good news is the reaction shows how much of a headwind the trade situation is on the market right now. It's like a coiled spring ready to react to a whiff of good news. The bad news is it needs to be more official and less floated," said Art Hogan, chief market strategist at National Securities.

Caterpillar shares spiked 2.2 percent, while Boeing jumped 2 percent. Caterpillar and Boeing shares are seen as bellwethers for global trade given their exposure to overseas markets. Apple also rose 0.6 percent.