North Korea state media said Monday that "ceaseless large-scale war games" by the US and South Korea are "creating a situation that a nuclear war may break out any moment."

Over the weekend, official sources from both North Korea and the US said the chances of war are growing.

"I think it's increasing every day, which means that we are in a race, really, we are in a race to be able to solve this problem," McMaster told an audience at the Reagan National Defense Forum in Simi Valley.

McMaster made the comment when asked if North Korea's launch of an intercontinental ballistic missile in the early hours of Wednesday morning local time had increased the chance of war.

"There are ways to address this problem short of armed conflict, but it is a race because he's getting closer and closer, and there's not much time left," McMaster said, referring to North Korean leader Kim Jong Un.

With every missile launch or nuclear test, Kim has improved his country's capabilities, McMaster said.

"I think we're really running out of time," he said.

Graham also said he will urge the Pentagon not to send any military dependents to South Korea.

"It's crazy to send spouses and children to South Korea, given the provocation of North Korea. So I want them to stop sending dependents. And I think it's now time to start moving American dependents out of South Korea," he said.

Air combat exercise begins

Six US Air Force F-22 Raptors, Washington's top-of-the-line stealth fighters, arrived in South Korea on Saturday to participate in the Vigilant Ace 18 air combat exercise, an annual US-South Korea drill the US Air Force says is designed to boost the "combat effectiveness" of the alliance.

"The US aircraft that have landed on South Korea include six F-22s, six F-35s, six EA-18Gs," a South Korean defense official told CNN. "More than 10 F-15Cs and F-16s have also been deployed for the drill."

These aircraft will stay in South Korea for the week. They will be joined by more F-35Bs -- the Marine Corps version, based in Japan -- B-1 bombers and E-3 airborne warning and control system (AWACS) aircraft that will fly in to join the war games and then return to bases elsewhere, the official said.

But it is the stealth fighters that experts say pose the biggest threat to Pyongyang.

While the North Korean military maintains capable anti-air weaponry, its radar systems would be unable to detect the F-22s and F-35s, which are cloaked with the world's most advanced stealth coating, before a strike on those defensive systems.

The North Korean commentary published in state newspaper Rodong Sinmun on Sunday said the aerial war games show "the enemies' moves to start a nuclear war have reached a dangerous stage."

"It is an open, all-out provocation against the DPRK, which may lead to a nuclear war any moment," it continued.

It said war games are "driving the situation of the Korean Peninsula to the lowest ebb" and "bringing dark clouds of a nuclear war to the Korean Peninsula and Northeast Asia."

North Korean threat to US mainland

The exercises come less than a week after Pyongyang fired off an intercontinental ballistic missile it claims can reach the "whole" mainland of the United States.

It is likely the ballistic missile, fired higher than any previous North Korean missile, broke up as it re-entered Earth's atmosphere, the official said.

Still, the ability of the new missile to fly higher and longer than others in the past signals North Korea's intent to develop weapons capable of attacking the US.

At the California forum, McMaster said Kim was extremely unlikely to change his behavior "without some significant new actions in the form of much more severe sanctions" and "complete enforcement of the sanctions that are in place."

He pushed China to do more, including cutting off North Korean oil imports.

"We're asking China not to do us or anybody else a favor," he said. "We're asking China to act in China's interest, as they should, and we believe increasingly that it's in China's urgent interest to do more."