North Korea, after conducting two ICBM tests last month, claimed the “whole U.S. mainland” is now within range.

The U.S. is willing to talk to North Korea provided it agrees to the condition that such talks will move towards its de-nuclearisation, Secretary of State Rex Tillerson said on Tuesday, reiterating the U.S. position that has so far been unacceptable to Pyongyang.

Mr. Tillerson did not rule out a military strike against North Korea in remarks that were overall not strident, at the State Department on Tuesday.

Rooting for a diplomatic breakthrough in a crisis that is snowballing fast as the first major test for the six-month old administration of President Donald Trump, Mr. Tillerson said, “We have reaffirmed our position towards North Korea, that what we are doing, we do not seek a regime change; we do not seek the collapse of the regime; 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. [border between North and South Koreas]… And 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.”

North Korea has conducted two intercontinental ballistic missile (ICBM) tests last month and its leader Kim Jong-un has claimed the “whole U.S. mainland” is now within range. The U.S. has taken the threat seriously, and last month National Security Adviser (NSA) H.R. McMaster said war plans were underway, at the instruction of the President.

CIA Chief Mike Pompeo said recently that a regime change could also be an option. U.S. and its allies flew bombers over the Korean peninsula in a show of strength on Sunday, after the second ICBM test.

As tensions grow, South Korean President Moon Jae-in has agreed to deploy more missile interceptor systems — American-made Terminal High Altitude Area Defense or THAAD — in response, indicating a turnaround in his position. Around 30,000 American troops are located in South Korea, which will be the first target of any North Korean retaliation.

Meanwhile, Republican Senator Lindsey Graham said on Tuesday that Mr. Trump has assured him that if “thousands die,” they will die in North Korea, and not in America. “There is a military option to destroy North Korea's [missile] programme and North Korea itself… If there's going to be a war to stop them, it will be over there. If thousands die, they're going to die over there, they're not going to die here and [President Donald Trump] told me that to my face,’ Mr. Graham told a TV show.

Responding to Mr. Graham’s remarks White House Press Secretary Sarah Huckabee Sanders said, “The President obviously has been very outspoken about how he feels about North Korea. We are weighing all options, keeping all options on the table, and as we have said many times, we are not going to broadcast what we are going to do.”

Mr. Tillerson also made overtures to China, citing its “unique” relationship with North Korea and seeking its help to turn the situation. President Donald Trump has been expressing his disappointment with China in hostile terms in recent weeks, as North Korea continued with its missile testing.

Mr. Trump’s repeated calls to China is possibly meant to effectively call its bluff, according to some observers. In the event of a war, Mr. Trump could blame China for its inability or unwillingness to rein in North Korea.