New York (CNN Business) Stocks rallied all the way into the close on Tuesday, both in the United States and elsewhere, as positive sentiment about trade took hold of the market.

President Donald Trump tweeted this morning to inform the public about a "very good telephone conversation" with Chinese Premier Xi Jinping. He said the two leaders would meet at the G20 summit in Japan next week.

Trump previously said that China would face additional import tariffs if Xi didn't show up to the summit.

Dow INDU S&P 500 SPX Nasdaq Composite COMP That gave stocks a boost that lasted all day. Thewas up by more than 400 points at its high. It ultimately closed up 353 points, or 1.4%. Theand thefinished 1% and 1.4% higher, respectively. European stocks also closed in the green.

For the month, the Dow and the S&P are up 6.7% and 6%, respectively. The Nasdaq is on track for a 6.7% jump this month. At this point, June is the best month for stocks since January.

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