Taking president Donald Trump at his word, Wall Street staged another rally Tuesday with the Dow Jones Industrial Average, the S&P 500 and the NASDAQ Composite all showing signs of more life.

The Dow rose by more than 400 points at its peak on Tuesday, before eventually closing at 353 points, or up 1.4 percent. The S&P 500 and the NASDAQ gained 1 percent and 1.4 percent, respectively. European stocks also had a good day and closed on the upside.

As of Tuesday, the Dow and the S&P are up 6.7 percent and 6 percent, respectively. On the other hand, the NASDAQ remains en route to a 6.7 percent jump for the entire month. Analysts agree June is the best month for stocks since January 2019.

Catalyst for another day of optimism at the Street was a tweet by Trump Tuesday morning about a "very good telephone conversation" he said he had with Chinese president Xi Jinping. Trump again said he and Xi will meet at the G20 summit in Osaka, Japan next week. This simple tweet was enough to give stocks a boost that lasted all day Tuesday.

China confirmed Trump’s phone call with Xi on Tuesday, and said Trump had requested he be allowed to call Xi. The Chinese leader told Trump he stands ready to meet with him in Osaka to exchange views on fundamental issues about the development of China-U.S. relations.

Official Chinese state-run media said Xi admitted some difficulties recently occurred in China-U.S. relations were not in the interests of either side. Xi told Trump their countries will benefit from cooperation and lose from confrontation.

He also said China and the U.S. must (in accordance with a consensus he previously reached with Trump), push forward the China-U.S. relationship based on coordination, cooperation and stability on the basis of mutual respect and mutual benefit.

Xi Jinping
Chinese President Xi Jinping waits for British Prime Minister Theresa May (not pictured) ahead of their meeting at Jinping's official Diaoyutai State Guesthouse on Feb. 1, 2018 in Beijing, China. Getty

As for economic and trade issues, Xi emphasized both countries should solve their problems through dialogue on an equal footing. He said the key to success is being able to accommodate each other's legitimate concerns. He also hopes Trump can treat Chinese firms in a fair manner.

Xi wants to have both countries' trade teams maintain contact on how to solve the trade war.

Trump two weeks ago said China will face additional import tariffs if Xi didn't show up at the G20 summit.

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