North Korea’s launch last week of a type of missile that may soon be able to deliver a nuclear warhead to the United States mainland set off the Trump administration on a troubling new trajectory.

In the space of a week:

■ Nikki Haley, the United States ambassador to the United Nations, warned that tensions with North Korea made it an “open question” whether American athletes would be able to compete in the Winter Olympics in South Korea in February. (The White House press secretary, Sarah Huckabee Sanders, later said that while there had been no official decision on participating, “the goal is to do so.”)

■ Lt. Gen. H. R. McMaster, the national security adviser, said the risk of war with North Korea was “increasing every day, which means that we are in a race, really, we are in a race to be able to solve this problem.”

■ Senator Lindsey Graham of South Carolina, a Republican leader on national security, warned that “we’re getting close to a military conflict” and that the Pentagon should stop sending the families of the 28,000 American troops in South Korea to live with them at military bases there.