South Korean stocks also climbed, with the iShares MSCI South Korea capped exchange-traded fund (EWY) popping 1.9 percent. The index was also on track to post its biggest one-day gain since May 8, when it gained 2.55 percent. The EWY dropped 4.57 percent last week.
Stocks were also helped by signs global growth is chugging along. The Japanese economy posted better-than-expected economic growth for the second quarter, growing at an annualized rate of 4 percent.
"We're also getting more signs of synchronized economic growth around the world," said Kate Warne, investment strategist at Edward Jones. "Markets around the world are going up today. It's a risk-on day across the board."
Investors also dumped safe-haven asset gold, as futures for December delivery fell $3.60 to settle at $1,290.40 per ounce after hitting a two-month high last week.
"In our experience, geopolitical shocks tend to provide a buying opportunity, unless there is: an underlying economic slowdown (as was the case prior to Iraq invasion of Kuwait); clear cut overvaluation; or a monetary tightening," wrote Andrew Garthwaite, Credit Suisse global equity strategist, in a note to clients. "Even if the main proponents' behaviour may appear aggressive, their advisors and sponsors are likely to act as an ameliorating force."
The CBOE Volatility Index (VIX), widely considered the best gauge of fear in the market, traded near 12.4, down about 20 percent. The index posted its largest weekly gain since December 2015 last week as the North Korea situation escalated with strong warnings from President Trump.
"August has been historically bullish for volatility, although we'll likely need to see some smoothing out of the movement in the VIX before another spike occurs, albeit a macro event like action taken in North Korea or other 'black swan'-type events," said Andrew Thrasher, portfolio manager at the Financial Enhancement Group.
Meanwhile, no major data is set to come out on Monday.
In Europe, stocks traded in the black, with the Stoxx 600 index advancing 1.1 percent, while Asia markets finished trade on a mostly positive note on Monday, after investors digested another batch of data.
—CNBC's Sam Meredith and Javier E. David contributed to this report.
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