Washington (CNN) US ambassador to the UN Nikki Haley says President Trump's tweet warning North Korean leader Kim Jong Un about US nuclear capabilities helps global security because it keeps Kim "on his toes."

"We want to always remind them we can destroy you, too, so be very cautious and careful with your words and what you do," Haley said Sunday on ABC's "This Week ."

The latest war of words between the two leaders began when Kim, in a New Year's speech , signaled his willingness to engage in talks with South Korea and claimed the entire US mainland was within range of North Korean missiles. "The nuclear button is always on the desk of my office," he said. "They should accurately be aware that this is not a threat but a reality."

Trump responded via Twitter, saying, "I too have a Nuclear Button, but it is a much bigger & more powerful one than his, and my Button works!"

Sanctions and "other" pressures are beginning to have a big impact on North Korea. Soldiers are dangerously fleeing to South Korea. Rocket man now wants to talk to South Korea for first time. Perhaps that is good news, perhaps not - we will see!

Critics said Trump's tweet was too flippant and raised new questions about whether he understands the gravity of a potential nuclear war . But Haley said Sunday that Trump's wording was an appropriate response to Kim's statement.

"He can't sit there and imply that he's gonna destroy the United States without us reminding him of the facts and the reality that if you go there it's not us that's going to be destroyed, it's you," Haley said.

"I think that he (Trump) always has to keep Kim on his toes."

Pompeo weighs in

CIA Director Mike Pompeo made a similar argument about Trump's tweet in an interview on "Fox News Sunday" and said it was part of a strategy that broke with decades of unsuccessful US policy toward North Korea.

"That tweet is entirely consistent with what we're trying to communicate," Pompeo said. "We want the regime to understand that unlike before, we are intent on resolving this. And it is our firm conviction that resolving this diplomatically is the correct answer, but that this administration is prepared to do what it takes."

South Korea reacted positively to Kim's statement expressing a desire for talks between the north and south, and person-to-person talks between the two nations are set for Tuesday.

Pompeo expressed skepticism that the talks would lead to a permanent solution to the conflict between the two countries, but said, "we'll just have to wait and see" before rendering final judgment.

For her part, Haley said she believed the talks would focus only on the upcoming Winter Olympics in South Korea, which Kim wants to participate in. But she added it would be positive if the two sides can "at least start getting back into talks."

Haley said Trump's tweets and actions help get the attention of world leaders who "see him as unpredictable."

"I don't think they know what the US is going to do at any given time," she said.

Trump said Saturday he was open to talks with North Korea, but added there would be prerequisites. Haley elaborated on Sunday, saying North Korea would need to take "a lot" of steps -- such as suspending its weapons tests and be willing to talk about ending its nuclear program -- before Trump would agree to talks.

But she added that North Korea would not need to meet both of those conditions before potential talks.

"I think stop testing is very important, and for a very significant amount of time. And then you go and you work toward the next step," Haley said. "This is going to be phases."

Iran protests

Meanwhile, recent protests in Iran have drawn the attention of much of the world -- and the strong support of the Trump administration.

The Iranian government has responded to the protests with force in some areas, and Iranian leaders have accused the US of backing the anti-government protesters.

Pompeo on Sunday said it is "false" to say CIA is behind the protests.

"This was the Iranian people, started by them, created by them, continued by them, demanding a better set of living conditions and a break from the theocratic regime that has been with them since 1979," he said.

Pompeo reiterated Trump's support for those protesting the Iranian government and said he expected people in Iran to continue to "revolt" in the future.