During a visit to South Korea, he also said the US was exploring a range of new diplomatic and economic measures.
He also defended the deployment of a US missile system in South Korea.
The move has angered China, but South Korea and the US say the system is needed to defend against North Korea.
Mr Tillerson spoke shortly after visiting the demilitarised zone which divides the two Koreas.
He arrived in South Korea from Japan, where he said that 20 years of efforts aimed at persuading North Korea to abandon its nuclear ambitions had failed.
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 said: "If they elevate the threat of their weapons programme to a level that we believe requires action, then that option's on the table."
Mr Tillerson also 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.
The US accuses 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 regime and potentially create chaos on its border.
China is also strongly opposed to the deployment of the Terminal High Altitude Area Defense (Thaad) system in South Korea.
The US says the system is aimed at countering the threat from Pyongyang, but China says its powerful radar 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.
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