WASHINGTON—The U.S. intends to expand offensive operations in cyberspace to counter digital economic espionage and other commercial hacks, White House national security adviser John Bolton said Tuesday, while also dismissing talk of a split with President Trump on North Korea and other hot spots.

Mr. Bolton said recent U.S. offensive cyber operations, conducted since Mr. Trump relaxed restrictions last year, had been primarily focused on stopping election interference. But the U.S. is now broadening its efforts to counter...