Speaking to reporters Monday, Defense Secretary James Mattis said North Korea is "intentionally doing provocations that seem to press against the envelope for just how far can they push without going over some kind of a line in their minds that would make them vulnerable".
At the same time, Mattis appeared unwilling to discuss the matter, saying he "will not go into details" about USA military options and that "I don't want to go into that".
Mattis also said there are military options the USA can take with North Korea which would not put the South at serious risk, but he refused to explain such options in detail.
It "would elicit a different response from us", if a North Korean missile were to threaten USA or Japanese territory, he said.
Pressed on whether that might include so-called "kinetic" options that use lethal force, Mattis said: "I don't want to go into that".
The Pentagon is looking at potential covert cyberattack options.
"Military options available to Trump range from non-lethal actions like a naval blockade aimed at enforcing sanctions to waging cyber attacks and positioning new USA weaponry in South Korea, where the United States has 28,500 troops".
When asked whether it was possible that such nukes might be deployed to the Korean Peninsula, Mattis said the two sides had "discussed the option", but declined to elaborate.
South Korea has raised the possibility of reintroducing nuclear weapons to the peninsula.
The United States and its allies have been scrambling to respond to North Korea's accelerating nuclear program, which appears to be growing more sophisticated.
President Trump has repeatedly refused to rule out a military strike on North Korea's nuclear facilities. China in turn favors an worldwide response to the problem.
Meanwhile, Mattis confirmed that Washington will not be shooting down North Korean missiles unless they pose a direct threat to the US.
Even as tensions rise, the United States and its allies have stuck to a hands-off policy when North Korea test-fires its missiles.
The North has repeatedly defied the United Nations to conduct nuclear and missile tests, the latest being a mid-range missile fired over Japan on Friday, soon after the reclusive nation's sixth and most powerful nuclear test on September 3.