But he called on other countries to isolate the country diplomatically.
The foreign minister of China, North Korea's greatest ally, said a peaceful settlement was the "only right choice".
Mr Tillerson told a UN Security Council meeting that the threat of North Korea launching a nuclear attack on its neighbours was "very real".
Thousands of US soldiers are stationed in North Korean neighbours South Korea and Japan.
'The right agenda'
Asked by US broadcaster NPR if the US was prepared to hold direct talks with North Korea, Mr Tillerson replied: "Obviously, that would be the way we would like to solve this.
"But North Korea has to decide they're ready to talk to us about the right agenda."
He called on UN member states to implement sanctions on North Korea or downgrade diplomatic relations with the country.
Speaking to the UN Security Council, he said the US would use diplomatic and financial measures against North Korea - including potential sanctions on companies or individuals with ties to North Korea - but would be willing to consider military action if necessary.
For years, he said, North Korea had dictated the terms of its dangerous course of action.
"It's time for us to retake control of the situation," he said. "The threat of a North Korean nuclear attack on Seoul or Tokyo is real, and it is likely only a matter of time before North Korea develops the capability to strike the US mainland."
Speaking to reporters ahead of the UN meeting, Chinese Foreign Minister Wang Yi said the situation on the Korean peninsula was "at a critical point".
"Peaceful settlement of the nuclear issue on the Korean Peninsula through dialogue and negotiations represents the only right choice that is practical and viable," he added.
He also repeated a Chinese offer to halt Pyongyang's military programme in return for a freeze on joint US-South Korea military drills.
The US has rejected the idea in the past, saying the nuclear programme must be halted first.
North Korea has made repeated attempts to miniaturise nuclear warheads and fit them on long-range missiles capable of reaching the US.
It has also made several military shows of strength in recent weeks and the US has sent warships and an anti-missile system to the region in response.
Earlier on Friday, he told the US radio network NPR he was seeking denuclearisation, not seek regime change. And in a wide-ranging interview with Reuters, US President Donald Trump said he feared a "major, major conflict" if negotiation attempts did not work.