Haley, speaking on CNN's State of the Union, said, "We have pretty much exhausted all the things that we could do at the Security Council at this point."
Haley told CNN's Dane Bash she would be "perfectly happy" turning things over to U.S. Defense Secretary Jim Mattis.
"We wanted to be responsible and go through all diplomatic means to get their attention first," Haley said. "If that doesn't work, General [Jim] Mattis will take care of it."
Last Monday, the U.N. Security Council adopted a new round of sanctions on North Korea after the nation's sixth and largest nuclear weapons test. On Thursday, North Korea fired a ballistic missile that flew over Japan in the North Pacific and reached a height of 478 miles and distance of about 2,300 miles.
On Friday, Haley told reporters at the White House that North Korea has been "strangled" by sanctions and said military options remain squarely on the table if sanctions are not effective.
On Sunday, she reiterated those views.
"If North Korea keeps on with this reckless behavior, if the United States has to defend itself or defend its allies in any way, North Korea will be destroyed," Haley said. "And we all know that, and none of us want that."
Last month, U.S. President Donald Trump said North Korea "will be met with fire and fury and, frankly, power, the likes of which this world has never seen before" if Kim Jong Un continued to threaten the United States.
"You have to ask the president what fire and fury meant," Haley said. "But I think we all know that, basically, if North Korea keeps on with this reckless behavior, if the United States has to defend itself or defend its allies in any way, North Korea will be destroyed."
On Sunday morning, Trump called the North Korea leader "Rocket Man," which was a 1972 song sung by Elton John.
He posted on Twitter: "I spoke with President Moon of South Korea last night. Asked him how Rocket Man is doing. Long gas lines forming in North Korea. Too bad!"
"We are out of road because in the past the approach taken to the problem of North Korea and the Kim regime over decades has been to enter into long drawn-out negotiations that then deliver an unsatisfactory agreement -- an agreement that then the North Korean regime breaks," McMaster said.
McMaster said Trump's scheduled speech Tuesday at the U.S. General Assembly in New York will "communicate his vision for America's role in the world" in three areas: protecting American people, promoting American prosperity and promoting accountability and sovereignty.