Washington (CNN) Secretary of State Rex Tillerson said that the US is willing to sit down for talks with North Korea, but only if it relinquishes its pursuit of nuclear weapons.

Tillerson, speaking at the State Department press briefing, stressed that the US was not seeking regime change or looking to send its military "north of the 38th parallel" that divides North and South Korea. But he emphasized that the danger posed by Pyongyang, which test fired two intercontinental ballistic missiles in July, was unacceptable.

"We do not seek regime change. We do not seek an accelerated reunification of the peninsula. We do not seek an excuse to send our military north of the 38th parallel," Tillerson said during a surprise visit to the agency's briefing room on Tuesday.

"We are not your enemy, we are not your threat, but you are presenting an unacceptable threat to us and we have to respond," Tillerson said, speaking to North Korea directly. "We would like to sit and have a dialogue about the future."

"Our other options," Tillerson added, "are not attractive."

A willingness to talk if North Korea agrees to pursue denuclearization was also Obama administration policy, though it was never successful in getting Pyongyang to the table , and some analysts have questioned whether assumptions North Korea may be willing to scale down its arsenal are out of date.

Tillerson spoke about a series of challenges across the global stage , touching on Syria and the fight against ISIS, Iran's destabilizing activities in the Middle East and efforts to reach a peaceful resolution of the conflict in eastern Ukraine, the site of clashes between Russian-backed rebels and government troops.

The goal of all US foreign policy now, he said, was to make good on President Donald Trump's campaign slogan to "make America great again."

"That's not just a slogan," Tillerson said. "It is what guides our formulation" of policy, he said. But Tillerson cautioned that, "When we say 'America First,' it doesn't mean America alone."

The former ExxonMobil CEO said that dealing with potentially disruptive tweets from Trump, who has sent out 140-character blasts that have contradicted positions Tillerson has taken publicly, is just part of the job.

"It's part of the environment in which we work, we'll adapt to it," Tillerson said. "There's a lot of unexpected things that happen to us in the world of diplomacy. ... Whatever the President chooses to express, he expresses to everybody."

In July, Tillerson was asked at a gathering of oil executives whether Trump's tweets complicate his work, and he told them that the job was more "difficult" than his previous one.

"A good relationship"

Asked Tuesday about his relationship with Trump, Tillerson said, "We have a good relationship ... he calls me late at night on the weekends. ... It is a very open relationship and it's one in which I feel quite comfortable telling him my views."

He admitted that, "We have differences," naming the Iran nuclear pact as one of them. "If we did not have those differences, I would not be serving him."

The bulk of Tillerson's comments, though, were about policy, not politics.

Tillerson took aim at the international nuclear pact with Iran, the Joint Comprehensive Plan of Action, saying that it dealt with only a very thin slice of the issues that the US has concerns about.

Trump only reluctantly certified in July that Iran is complying with the deal, and the administration has been signaling that it might walk away from the pact, reached under the Obama administration along with France, the UK, Germany, China and Russia.

"The conversation on Iran does not begin and end with the JCPOA," Tillerson said the agreement ignored other problems Iran causes, citing the way Tehran exports fighters into Syria and Iraq as well as Iran's support for Houthi rebels in Yemen.

"It was kind of like we put blinders on and ignored all the other things," when the agreement was negotiated, he said. He insisted that "the spirit of the agreement has been violated" because Iran has not been a "good neighbor" to other countries in the region.

"It's an agreement ... that should serve Americans interests first and foremost, and if it doesn't serve those interests why would we keep it?" Tillerson said.

The top US diplomat also said he was sending the former head of Central Command, retired Gen. Anthony Zinni, to the Middle East to help resolve a standoff between the US' Gulf allies that led Saudi Arabia, Bahrain, Egypt and the UAE to cut ties with Qatar and accuse Doha of supporting terrorism.

The issue became an instant problem for the administration because the largest US base in the Middle East is based in Qatar. Zinni will go to the region "so we can maintain a constant pressure on the ground," Tillerson said. "There's only so much you can do with telephone persuasion."

Tillerson said that "Qatar is fulfilling its commitments" under an agreement Doha reached with the US on fighting terrorism financing. "We are committed to seeing this dispute resolved," Tillerson said, adding that the US sees it as "important to the fight against terrorism."

Russia tensions

Tillerson was asked about simmering tensions with Russia , which just announced it is expelling US diplomats. He said he would meet this week with Russian Foreign Minister Sergei Lavrov on the margins of meetings in Asia to discuss improving ties with Russia in light of new sanctions legislation passed by Congress.

Tillerson said the legislation expresses the will of the American people. "We'll just work with it," he said. "We can't let it take us off track" when it comes to improving the relationship.

One area of cooperation with Russia is in the fight against ISIS, he said. He said the anti-ISIS "coalition has achieved remarkable success" since Trump took office.

He also touched on Latin America, saying that the US is "very, very troubled" by events in Venezuela, where opposition leaders were taken into custody after an election that created a legislative body made up entirely of supporters of President Nicolas Maduro.

Tillerson urged Venezuela to "return to its constitution, return to its scheduled elections," and said the opposition leaders' arrests were "very alarming."

"We are evaluating all of our policy options as to what we can do," he said.

But Tillerson's first order of business was North Korea, which the administration has made a priority. Last month, Pyongyang threatened a nuclear strike on "the heart of the US" if it tries to remove Kim Jong Un.

Tillerson said the threat from North Korea has "materialized in the ways we expected it would" and that the administration's first response has been to initiate "a sustained and continued intensified campaign of what I like to call peaceful pressure."

Tillerson travels to Asia later this week, where he will continue his drive to increase "peaceful pressure on the regime in North Korea to have them develop a willingness to sit and talk to us and others," but with an understanding that there's no possibility of talks if North Korea doesn't abandon its nuclear program.

He said that China has a particular role to play, as it accounts for 90% of trade with North Korea. Trump had emphasized that point as he courted Chinese President Xi Jinping during a state visit and pressured Beijing to use its influence on Pyongyang.

More recently, Trump has expressed disappointment that Beijing hasn't applied as much pressure as he'd like or caused a change in North Korea's behavior.

Arguing that China sees eye-to-eye with the US about the threat posed by Pyongyang's aggressive weapons development, Tillerson said, "We certainly don't blame the Chinese for the situation in North Korea."

"But we do believe China has a unique and special relationship," he added. "We continue to call upon them to use that influence with North Korea to create the conditions where we can have a productive dialogue."

North Korea doesn't "define" the US-China relationship, he insisted, but he added that ties between Washington and Beijing are at an important "pivot point."