In the past 24 hours, Trump promised "fire and fury like the world has never seen" if Pyongyang escalated the nuclear threat it poses.
"Look North Korea, leave Guam out of this!" he exclaimed.
The mixed messages from Tillerson and Trump put the onus on the North Koreans to decide how to interpret the latest missives from the U.S. Still, Tillerson insisted the developments didn't suggest the U.S. was moving closer to a military option to dealing with the crisis.
Trump's provocative remarks triggered reactions from other lawmakers too, who all said they were opposed to such a move.
"President Trump is not helping the situation with his bombastic comments", Democratic Senator Dianne Feinstein said in a statement.
Mr Trump told CNN: "If spoken to correctly - correctly - they will play ball".
"I think we are a long way off from nuclear war", Kennedy said.
Ministers adopt South China Sea code framework
She says the USA plans to discuss the issue with other Asian nations during a regional meeting taking place in the Philippines. Both diplomats spoke to the AP condition of anonymity because they were not authorized to discuss the issues publicly.
In a statement, House Democratic Leader Nancy Pelosi said President Trump's threat of "fire and fury" towards North Korea demonstrates weakness, not strength of objective.
He said: "You can never rule it out".
"That is empty rhetoric, the likes of which you always use", he said.
Mr Sullivan said if North Korea were to attack the USA first, Trump would have more authority to respond.
The US, in response, has ratcheted up the rhetoric and drafted a United Nations Security Council resolution that seeks to cut the country's $3 billion annual export revenue by a third.
"You start negotiating. If you don't stop them you will have to take rather drastic action because if you don't take them now, you're going to be in awfully big trouble in five years when they have more missiles than we do". Since early July, the North has tested two intercontinental ballistic missiles (ICBM), which it says can hit the U.S. mainland. "Talks, with the right expectation of what those talks will be about".