However, Trump didn't provide any specifics about his strategy towards Pyongyang.
Tillerson's statements come just a few days after North Korea tested a second intercontinental ballistic missile capable of reaching USA cities.
"We hope that at some point they will begin to understand that and we would like to sit and have a dialogue with them".
'He's told me that.
"The U.S. military has detected "highly unusual and unprecedented levels" of North Korean submarine activity and evidence of an 'ejection test, '" CNN added. You can stop North Korea, militarily or diplomatically, ' he said on NBC's 'Today Show'.
Asked about Graham's comments, White House Press Secretary Sarah Sanders initially repeated a statement the administration has used frequently in the past, "All options are on the table".
Russian Federation has condemned North Korea's recent ballistic missile provocation, but urged restraint and repeated calls for dialogue to resolve the North Korean issues.
Tillerson described the administration's strategy for dealing with North Korea as "peaceful pressure", stressing that less peaceful policy options are "limited, particularly if we think we're operating under a short period of time".
But he made it clear that there was no possibility of talks if North Korea did not abandon its nuclear programme.
But James Kim, a research fellow at the Seoul-based Asan Institute for Policy Studies, says Pyongyang's continued ICBM testing underscores its rejection of the United States approach.
"The goals are to stop the nuclear programme, stop the missiles, stop the aggression.
We do not seek an excuse to send our military north of the 38th Parallel".
Russia's new United Nations ambassador, Vassily Nebenzia, called North Korea's intensifying missile program "really serious", telling reporters the entire worldwide community is concerned and "we'll be working to see what we can do together in the council".
"Saying China can easily solve the problem is like saying peace in the Middle East is 'not as hard as people have thought, '" added the columnist, alluding to a comment made by Trump during a meeting with Palestinian Authority chairman Mahmoud Abbas last May. But we do believe China has a special and unique relationship because of this significant economic activity to influence the North Korean regime in ways that no one else can.
Tillerson said the United States has sought partnership with China to resolve the North Korean crisis, noting that China "accounts for 90 percent of North Korea's foreign trade".
Negotiations with the North Korean government are possible as long as there is "an understanding that a condition of those talks is 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 to the homeland".
"So that's really the objective", he said.