Asked if the possibility for military action existed, he said: "Certainly we do not want to, for things to get to military conflict."
But he added: "If they elevate the threat of their weapons programme to a level that we believe requires action, then that option's on the table."
North Korea has conducted nuclear and missile tests in recent years, and says it is close to testing long-range missiles capable of carrying nuclear warheads and reaching the US.
Big shift? Analysis by Stephen Evans, BBC News, Seoul
Mr Tillerson was blunt: the previous policy had ended. Despite that assertion, though, the difference between the Obama strategy and the Trump one is not obvious. Mr Obama had not ruled out military force and Mr Tillerson thinks sanctions might yet work.
Both administrations ruled out negotiation - though Mr Tillerson said they would be "premature" at the moment, prompting the thought that there might come a time when they were the right thing to do.
At the end of it, the situation remains the same: North Korea shows no hint of being willing to renounce nuclear weapons, whatever economic blows it receives and whatever China might think.
Mr Tillerson heads for Beijing next, hoping China will help - but in the past Mr Trump has called China an "enemy".
'Unnecessary and troubling'
The US has accused China, North Korea's main ally, of not doing enough to rein it in but Beijing remains wary of any action that could destabilise the North Korean government and potentially create chaos on its border.
During his address in Seoul, Mr Tillerson called on China to fully implement sanctions imposed by the UN in response to North Korea's nuclear and missile tests.
"I don't believe we have ever fully achieved the maximum level of action that can be taken under the UN Security Council resolution with full participation of all countries," he said.
China is also strongly opposed to the deployment of the Terminal High Altitude Area Defense (Thaad) system in South Korea. America says the system is aimed at North Korea but China says it will allow the US to spy on its territory.
In recent days there have been multiple reports of apparent economic retaliation aimed at South Korea by Beijing. Mr Tillerson called these actions "unnecessary and troubling".
"We also believe it is not the way for a regional power to help resolve what is a serious threat for everyone," he said.