Analysts said the lack of further rhetoric over the weekend had helped to calm the markets.
The gains in trade came in nearly every sector, led by technology and real estate stocks.
The Dow Jones Industrial Average, which measures 30 major US companies, rose 0.62% to 21,993.71.
The wider S&P 500 index was up 1% at 2,465.84, while the Nasdaq climbed 1.3% to 6,340.23.
On the Dow, major movers included Visa, which climbed 1.8% and Apple, which increased 1.5%.
Shares in Walt Disney sank 0.6% after Shonda Rhimes, the creator of shows such as Grey's Anatomy and Scandal, said she had signed a deal to create shows with Netflix. Ms Rhimes had previously worked with Disney's ABC.
US stocks rebounded on Monday, reversing some of the losses that were triggered last week by rising tensions between the US and North Korea.