Asked about President Donald Trump's tweeted threat that he has a bigger and more powerful "nuclear button
" than any weapons North Korean leader Kim Jong Un has at his command, Tillerson said North Korea understands that kind of rhetoric.
"I think the rhetoric that North Korea understands is that while it is our objective, and the President's been very clear, to achieve a denuclearization through diplomatic efforts, those diplomatic efforts are backed by strong military option if necessary," Tillerson said in an interview with CNN's Elise Labott.
"That is not the first choice and the President's been clear that's not his first choice, but it is important that North Koreans as well as every regional player understand how high the stakes are, in an effort to ensure our diplomatic efforts are fully supported," Tillerson said.
The top US diplomat said those diplomatic efforts are seeing success, with three UN Security Council resolutions passed to cut into North Korea's ability to export products that bring in valuable revenue, and to choke off its access to energy supplies.
Other countries have taken additional steps, he noted, closing down North Korea's diplomatic missions in their countries and announcing unilateral sanctions.
"I think it is a recognition that the President has demonstrated to the world how high the stakes are," Tillerson said. "That's why we must achieve a diplomatic outcome."
The aim is still to achieve the "complete, verifiable, irreversible denuclearization of the Korean peninsula," Tillerson said. Talks could bring positive outcomes for regional security and to North Korea itself.
Pyongyang "can actually chart a way for themselves to a more secure future, a more prosperous future for their people as well," Tillerson said.
"How we begin the talks has yet to be determined, but we clearly need a signal from North Korea that they understand these talks must lead to that conclusion."
If they don't, and they continue missile and nuclear tests, "the North Koreans have to understand that the penalties to them will continue and will only grow more severe."