But asked what if North Korea tests an intercontinental missile or nuclear device, she said, "I think then the president steps in and decides what's going to happen".
The official was referring to the 85th anniversary of the founding of its Korean People's Army, North Korea's military.
Meanwhile, the US submarine MI docked in Busan, South Korea, yesterday.
North Korea called the deployment of the "Carl Vinson" carrier group "an extremely unsafe act by those who plan a nuclear war to invade", and even vowed to sink the carrier with a "single strike".
Mr Trump told the council on Monday that the "status quo in North Korea is also unacceptable".
The comments came as Japan conducted exercises with a USA aircraft carrier strike group headed for Korean waters.
South Korea's Navy said it was conducting a live-fire exercise with U.S. Navy destroyers on Tuesday in waters west of the Korean Peninsula and would soon join the USS Carl Vinson aircraft carrier strike group approaching the region. Japan's Chief Cabinet Secretary Yoshihide Suga told reporters the three envoys were to deepen cooperation and ensure their countries stay on the same page amid growing tension.
The American president recently spoke with his Japanese, German and Chinese counterparts as tensions soar on the Korean Peninsula amid fears that Pyongyang is readying its sixth nuclear test.
Joseph Yun, the USA special representative for North Korea policy, told reporters in Tokyo that "China has a very, very important role to play" to convince its neighbor to abandon its nuclear program.
PHOTO, TOP: The USS Michigan, an Ohio-class nuclear-powered submarine, arrives at a naval base in Busan, South Korea, April 25, 2017. It did not elaborate.
KNWA - President Donald Trump is approaching his 100th day in office
At this point in 2009, President Obama's approval rating stood at 69%, with 26% disapproving of his job. Donald Trump was propelled to the White House as the president America despite political inexperience.
Tillerson will also head up a special meeting of the United Nations Security Council on Friday.
Meanwhile, the entire U.S. Senate has been invited to the White House for a briefing on Wednesday about the North Korea situation.White House Press Secretary Sean Spicer confirmed the upcoming briefing, for all 100 senators.
"It's bad for South Korea, it's bad for Japan, it's bad for China - you know they need to help us", he said.
"Until now, we have not observed any movements from the North that might indicate a direct provocation".
Trump on Monday urged the UN Security Council to consider stronger sanctions against Pyongyang, and United States senators will be briefed on North Korea at the White House on Wednesday.
The meeting follows a meeting the US President held with ambassadors from United Nations member states on the security council on Monday where he emphasised US resolve to stop North Korea's progress.
North Korea has so far conducted five confirmed nuclear tests and numerous missile test-launches. The Xi-Trump call on Monday morning Beijing time was the second time the two leaders have spoken by telephone since meeting in Florida earlier this month.
"They are at once perilously overestimating their own strength and underestimating the hazards they are brewing for themselves", it said.
The destroyer USS Wayne E. Meyers is conducting bilateral maritime exercises with a South Korean destroyer in waters west of the Korean Peninsula Tuesday and Wednesday, while the destroyer USS Fitzgerald is partnering with a Japanese destroyer in waters west of Japan, according to the US 7th Fleet.
USS Michigan, one of the largest submarines in the world, is more than 560 feet long and weighs more than 18,000 tons when submerged, according to the Navy.
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