Secretary of State Rex Tillerson speaks at the State Department on Tuesday, August 1, 2017 (Screengrab: State Dep't)

(CNSNews.com) – The United States “does not seek a regime change” in Pyongyang, and is not looking for a speedy reunification of the Korean peninsula or for “an excuse to send our military north of the 38th parallel,” Secretary of State Rex Tillerson said Tuesday.

“We’re trying to convey to the North Koreans, we are not your enemy, we are not your threat, but you are presenting an unacceptable threat to us, and we have to respond,” the administration’s top diplomat said during a rare appearance at the State Department’s regular press briefing.

Tillerson expressed the hope that message would get through, along with the message that “we would like to sit and have a dialogue with them about the future that will give them the security they seek and the future economic prosperity for North Korea.”

The nuclear-armed regime’s test-firing on Friday of an intercontinental ballistic missile (ICBM), the second in a month, moved the crisis to the top of the White House foreign policy priority agenda.

Tillerson appeared keen to dial down the temperature, hours after Sen. Lindsey Graham (R-S.C.) said President Trump has told him that “there will be a war with North Korea over their missile program if they continue trying to hit America with an ICBM.”

“There is a military option – to destroy North Korea’s program and North Korea itself,” the foreign policy hawk told the NBC’s Today show.

Graham said Trump would not allow “this madman to have a missile to hit America.”

“If there’s going to be a war to stop him, it’s going to be over there,” he said. “If thousands die, they’re going to die over there – and he’s told me that to my face.”

China’s role

Tillerson was not asked at the briefing about Graham’s remarks on Trump’s purported views, but a reporter did ask whether Trump’s use of Twitter to criticize China for not reining in its North Korean ally was complicating the secretary’s ability to do his job.

“With respect to how we conduct foreign policy in light of the fact that the president communicates the way he does – as I explained to the people in this building, look, it’s just like anything else. It’s part of the environment in which we work. We’ll adapt to it,” he replied.

“There’s a lot of unexpected things that happen to us in the world of diplomacy and we know how to adapt to that, we know to work with it. And so I don’t view it as an obstacle, a hindrance, or as an assistance. Whatever the president chooses to express, he expresses, and then that’s information to everybody, us included.”

Following the ICBM launch Trump – not for the first time – expressed his frustration about what he views as China’s failure to pressure North Korea to change its behavior.

“I am very disappointed in China,” he tweeted. “Our foolish past leaders have allowed them to make hundreds of billions of dollars a year in trade, yet ... they do NOTHING for us with North Korea, just talk. We will no longer allow this to continue. China could easily solve this problem!”

Tillerson, however, did not blame China – even as he prodded it to use its economic leverage with Pyongyang.

“We’ve been very clear with the Chinese we certainly don’t blame the Chinese for the situation in North Korea. Only the North Koreans are to blame for this situation,” he said.

“But we do believe China has a special and unique relationship, because of this significant economic activity, to influence the North Korean regime in ways that no one else can.”

Earlier, Beijing’s Xinhua state news agency described Trump’s linking of the North Korean issue and the U.S. trade deficit with China as “baseless.”

And a columnist in the People’s Daily, a Communist Party organ, wrote that “[w]hile China certainly has an important role to play in helping the two sides avoid a head-on collision, it is ridiculous to assume China has control over North Korea or is responsible for solving America’s security problem.”

“Saying China can easily solve the problem is like saying peace in the Middle East is ‘not as difficult as people have thought,’” added the columnist, alluding to a comment made by Trump during a meeting with Palestinian Authority chairman Mahmoud Abbas last May.