Markets in New York, Tokyo, Paris and Frankfurt avoided major swings, while the FTSE in London advanced 0.6 percent as the pound weakened against the dollar, the euro and other major currencies.
The move came after British Prime Minister Theresa May called for a two-year transition after Brexit in a major address. Dealers said the speech offered no new approaches to securing a favorable Brexit deal.
"Overall, there was very little detail or progress in this speech, with a risk of continued uncertainty among businesses and investors," Barclays said in a note. "Any continued delay in next week's negotiations may in turn dampen sentiment and the future investment and growth outlook."
Meanwhile, hot rhetoric between Washington and Pyongyang generated plenty of headlines but seemed not to trouble investors too much.
Trump, who threatened earlier this week to "totally destroy" North Korea, went after the country's leader again Friday on Twitter calling him a "madman" who "will be tested like never before!"
Earlier, Kim called the Trump a "mentally deranged US dotard" after the reclusive regime hinted it may explode a hydrogen bomb over the Pacific Ocean.
Russian Foreign Minister Sergei Lavrov described the rhetoric between leaders of the United States and North Korea as a "kindergarten fight between children" and urged calm.
Markets seemed to have the same attitude.
"The markets no longer pay attention to what Trump says," said Gregori Volokhine, president of Meeschaert Capital Markets. "They're waiting to see what Trump does."
Among individual stocks, Apple fell 1.0 percent as its latest smartphone, the iPhone 8, arrived in stores. Some analysts think sales of the device will be weak due to the impending introduction of the even more richly endowed iPhone X, which will hit shelves in November.
Fiat Chrysler shares rose 3.3 percent in New York, lifted by speculation that Korean carmaker Hyundai is interested in taking over the US-Italian company.
Shares in French cosmetics giant L'Oreal jumped nearly three percent as investors bet on a possible ownership change at the company following the death Wednesday of the French cosmetic company's heiress Liliane Bettencourt, who was 94.