U.S. Secretary of State Rex Tillerson said Tuesday that the U.S. is willing to talk with North Korea -- but only if North Korea gives up its pursuit of nuclear weapons.

"We felt the appropriate thing to do first was to seek peaceful pressure on the regime of North Korea, to have them develop a willingness to sit and talk with us and others -- but with an understanding that a condition of those talks is that there is no future where North Korea holds nuclear weapons or the ability to deliver those nuclear weapons to anyone in the region, much less to the homeland," Tillerson said at a press briefing.

As for China, Tillerson said the country is in "special and unique relationship" when it comes to influence over North Korea. Still, the U.S. knows "only the North Koreans are to blame" for its standing in the international community.

Tillerson struck a more conciliatory tone than some of President Trump's tweets about China this weekend. Mr. Trump tweeted that he is "very disappointed" in China for doing "nothing" in relation to North Korea. The Trump administration has warned of possible economic repercussions for China for continuing to trade with North Korea. China accounts for 90 percent of North Korean trade.

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Chinese Ambassador Liu Jieyi said Monday that the U.S. and North Korea hold "the primary responsibility" to de-escalate tension and negotiate peace on the peninsula.

North Korea last month successfully tested a intercontinental ballistic missile (ICBM) capable of reaching the U.S. On Friday, North Korea launched another ICBM, and flight patterns indicate it landed close to where an Air France flight had flown less 10 minutes earlier.