He said the USA does not want a military conflict, but if North Korea takes actions that threaten South Korean or United States forces it would be met with an "appropriate response".
Mr Tillerson added that any action by Kim Jong-Un's regime which threatens South Korea will be met with "an appropriate response".
Tillerson said that the US has provided $1.3 billion in resistance to the authoritarian regime since 1995, but "in return North Korea has detonated nuclear weapons and dramatically increased its launches of ballistic missiles to threaten Americana and our allies".
North Korea recently launched four missiles, with the apparent, and unsuccessful, aim of hitting US airbases in Japan.
U.S. Secretary of State Rex Tillerson arrived in Beijing on Saturday afternoon, ... the third and final destination of his first trip to Northeast Asia as the Trump administration's top diplomat.
Wrapping up his comments on the controversy, Tillerson explained that, "The host country decides whether we are going to do things or not".
North Korea has a long-standing ambition to become a nuclear power, saying it needs to be able to defend itself, and conducted its first underground atomic test in 2006, in the teeth of global opposition. He also endorsed the "One China" policy, which has governed relations between the United States, China and Taiwan for decades, after questioning its legitimacy shortly after his election. Presumably the U.S.is also continuing cyber-attacks against the North Korean nuclear program.
Record 7 Croatian Representatives in Champions League Quarterfinals
Zidane said he had no preferences whether he would rather win the Spanish league or the Champions League with Madrid . This weekend they travel to the Basque country to take on Athletic Bilbao, while Barca play at home to Valencia.
In talks with Mr Xi in Beijing on Sunday, Mr Tillerson said Mr Trump places a "very high value" on communications with the Chinese president via phone calls and exchanges of letters.
The latest bout of tension with North Korea comes at a time of political turmoil in South Korea.
"We know that through further dialogue we will achieve a greater understanding that will lead to a strengthened, strengthening of the ties between China and the United States and set the tone for our future relationship of cooperation".
Trump had branded China a currency manipulator stealing American jobs and also threatened to impose 45 per cent tariffs on Chinese goods.
Last week, it launched four more ballistic missiles and is working to develop nuclear-tipped missiles that can reach the United States.
China, however, has accused Washington of escalating tensions by holding military exercises with its ally Seoul and deploying an anti-missile system in South Korea.
However, China has been angered by the deployment of a USA missile defence system to the South.
The two sides appear to have toned down differences as they work on finalising a trip by Xi Jinping to the U.S., possibly next month, for his first summit with Donald Trump.