WASHINGTON -- US Defense Secretary Jim Mattis warned North Korea Wednesday to stop provocations that could bring destruction to its regime and its people.

The rebuke comes as tensions have heightened over North Korea's threats to strike the US with nuclear weapons.

"The DPRK should cease any consideration of actions that would lead to the end of its regime and the destruction of its people,"

Mattis said in a statement. DPRK is the acronym of North Korea's official name, the Democratic People's Republic of Korea.

His warning is the latest in a series of aggressive statements exchanged between Washington and Pyongyang following the UN's adoption of tough sanctions over the weekend.

North Korea vowed to retaliate against the US as the resolution was pushed by Washington in response to the country's two tests of intercontinental ballistic missiles last month.

On Tuesday, US President Donald Trump threatened to unleash "fire and fury" if the communist nation continues to threaten his country. That warning came soon after The Washington Post, citing US intelligence officials, reported the North has successfully miniaturized a nuclear warhead to fit atop its missiles.

Undeterred, North Korea hit back, saying it is ready to carry out an attack on the US island of Guam, where US strategic military assets are stationed.

Mattis urged the defiant regime to stop isolating itself and "stand down" its pursuit of nuclear weapons.

"While our State Department is making every effort to resolve this global threat through diplomatic means, it must be noted that the combined allied militaries now possess the most precise, rehearsed and robust defensive and offensive capabilities on Earth," the secretary warned in the statement. "The DPRK regime's actions will continue to be grossly overmatched by ours and would lose any arms race or conflict it initiates."

He also issued a direct warning to North Korea's leader: "Kim Jong-un should take heed of the United Nations Security Council's unified voice, and statements from governments the world over, who agree the DPRK poses a threat to global security and stability."

In an early morning tweet, the president boasted about his country's nuclear arsenal.

"My first order as President was to renovate and modernize our nuclear arsenal," he claimed. "It is now far stronger and more powerful than ever before. Hopefully we will never have to use this power, but there will never be a time that we are not the most powerful nation in the world!"

Mattis backed up that tweet, saying the president's first orders to him upon taking office centered on maintaining the readiness of the US ballistic missile defense and nuclear deterrent forces.

En route home from a trip to Asia, Secretary of State Rex Tillerson assured Americans not to worry.

"I think Americans should sleep well at night, have no concerns about this particular rhetoric of the last few days," he told reporters on a flight to Guam, where he was to refuel, according to a transcript released by his department. "I think what the president was just reaffirming is the United States has the capability to fully defend itself with any attack, will defend our allies, and we will do so."

Sebastian Gorka, deputy assistant to Trump, interpreted the president's latest tweet as a warning to Pyongyang.

"He's saying, 'Don't test America and don't test Donald J. Trump,'" Gorka said in a Fox interview. "We are not just a superpower. We were a superpower. We are now a hyper power. Nobody in the world, especially not North Korea, comes close to challenging our military capabilities." (Yonhap)