On Saturday, North Korea warned that it was nearing its goal of reaching "equilibrium" in military force with the United States.
"We wanted to be responsible and go through all diplomatic means to get their attention first", Haley said.
This comes as about 200 world leaders, including President Trump, head to NY for the U.N.'s annual General Assembly. "None of us want war".
Tillerson said the U.S. strategy is to pursue a "peaceful pressure campaign" based on what he called the four "nos": not seeking either regime change or collapse in North Korea, an accelerated re-unification of the Korean peninsula, or a reason to send in military forces.
China's Foreign Ministry spokesman Lu Kang relayed the Chinese government's stance at a regular media briefing on Monday, when asked about U.S. Ambassador to the UN Nikki Haley's remarks on Sunday that the UN Security Council (UNSC) has exhausted its diplomatic options for dealing with North Korea.
The United States is far ahead of North Korea in terms of resources and capabilities, but a direct military confrontation with Pyongyang may still backfire, experts told Sputnik. "And at that point, there's not a whole lot the Security Council is going to be able to do", Haley said.
"I think that North Korea is not going to give up its program with nothing on the table", she said on CNN.
Also on Sunday, Rex Tillerson gave an interview to the program Face the Nation on CBS, in which he said that U.S. policy toward North Korea consisted of the "four no's", namely "we do not seek regime change, do not seek the regime's collapse, do not seek accelerated reunion ... of the peninsula", and that there are no plans to bring American forces north of the demilitarized zone (DMZ) separating the two Koreas.
Analysts have said the North has shown rapid improvements in its ballistic missile and nuclear technologies.
And Trump tweeted that he's asked Moon about "Rocket Man" - an apparent reference to North Korean leader Kim Jong Un. Looming behind them will be the prospect of renewed warfare on the Korean peninsula, with Ms Haley alluding to an official - Mr Mattis - who recently stressed America's ability to marshal and "overwhelming" and "massive" military response that could result in the "total annihilation" of North Korea.
"If our diplomatic efforts fail though, our military option will be the only one left", he said.
National Security Advisor H.R. McMaster echoed her sentiments telling Fox News it's time to stop kicking the can down the road because the U.S.is running out of road.
"We have tried a couple of times to signal to them that we're ready when they're ready", Tillerson added, "and they responded with more missile launches and a nuclear test". Recent missile tests have demonstrated the range to potentially strike the continental United States, along with the technical capacity to mount a miniature nuclear device on a missile, analysts said.
He said the pressure campaign is built around "putting together the largest and strongest worldwide coalition we can to send the same message to North Korea and to North Korea's neighbors, China and Russian Federation, that this is the policy of the rest of the world". Long gas lines forming in North Korea.