His statement comes just days after Pyongyang tested its second intercontinental ballistic missile, prompting a show of military force from both the US and South Korea.
Mr Tillerson repeated that Washington wanted to use peaceful pressure to persuade the rogue state to give up its missile and nuclear weapons programmes.
“We are not your enemy … but you are presenting an unacceptable threat to us, and we have to respond,” he told Pyongyang.
“We hope that at some point they will begin to understand that and we would like to sit and have a dialogue with them,” Mr Tillerson added.
For years North Korea has promised to develop a nuclear missile capable of hitting the US mainland – and recent tests indicate they may now be able to reach most of the country.
But for talks to be possible, Mr Tillerson said the country would need to give up their plans to develop nuclear weapons.
“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 the homeland,” he said.
Mr Tillerson also stressed that Washington is not seeking to replace the North Korean leadership.
“We do not seek a regime change, we do not seek a collapse of the regime, we do not seen an accelerated reunification of the peninsula, we do not seek an excuse to send our military north of the 38th parallel,” he said.
The secretary of state also repeated calls for China to help create the conditions for “productive dialogue” with its neighbour.
He described the other options available as “not particularly attractive”.
The Trump administration has repeatedly said that all options, including military action, are on the table when it comes to dealing with North Korea.
But a diplomatic solution is favoured, given the potential for massive casualties in South Korea and Japan – as well as among US troops stationed in the area – if Pyongyang retaliates.