The administration believes that doing so would force Pyongyang to the negotiating table.
While Tillerson did say that the USA needed "a period of quiet" before coming to the negotiating table, on Tuesday he invited North Korea to "talk anytime" - breaking with longstanding US policy by opening the diplomacy door even ifNorth Korea does not give up its nuclear weapons program.
"We're ready to talk anytime North Korea would like to talk, and we're ready to have the first meeting without precondition", Tillerson said. We can talk about whether there is gonna be a square table or a round table if that's what you're excited about.
"We want to work with Pakistan to stamp out terrorism within their boundaries as well, but Pakistan has to begin the process of changing its relationship with the Haqqani Network and with others".
The remarks, which followed North Korea's sixth nuclear test and two successful launches of intercontinental ballistic missiles this year, appeared to back away from a longstanding USA demand that Pyongyang must first accept that any talks would have to be about giving up its nuclear arsenal. Moreover, such a step would involve an ever-more intrusive inspection prying into all aspects of its military and security apparatus.
"Tillerson seems to have sent a message that all should boil down to direct talks between the US and North Korea", said Park Jeong-jin, vice director of the Institute for Far Eastern Studies.
And Heather Nauert, a spokeswoman for the State Department, tweeted to reiterate the administration position that preconditions apply regarding North Korea's nuclear programme. Pyongyang has pointed to the fate of Iraq and Libya-which bowed to United States demands over their weapons of mass destruction-only to be attacked.
The White House later issued a statement saying that Trump's position on the issue, for North Korea to surrender its weapons and cease missile testing altogether, has not changed.
The top diplomat's comments differ with Trump, who has said that Tillerson is "wasting his time" in trying to negotiate with North Korea.
Attention is also being placed on whether there will be contact between the USA and North Korea on the sidelines of an worldwide meeting on security to be held in Chiang Mai later this week.
Tillerson said the US has assured China that in the event that American troops had to cross north of the demilitarized zone separating the two Koreas, it would retreat back south once stability returned.
"Any successful diplomatic effort of has to be backed up with some type of military alternative", he further told the audience, arguing that "our military preparedness is strong".
"Pakistan has allowed so many terrorist organizations to find safe haven within its territories, and these organizations are growing in size and influence, that at some point I have said to the leadership of Pakistan, you may be the target, and they turn their attention from Kabul and decide they like Islamabad as a target better", said Tillerson.
Tillerson added USA military preparedness to respond to any North Korean threat was strong in the meantime. Last week, some 12,000 military personnel and more than 200 warplanes, including B-1B strategic bombers and the latest F-35 stealth fighters took part in major air drills.
"North Korea is acting in an unsafe way not only toward Japan, China, and South Korea, but the entire world". And what [does North Korea] want to put on the table?
Reported by RFA's Korean Service. These three conditions reconfirm the so-called Tillerson plan, which was announced before North Korea's recent ICBM launch.
After his four-day visit, the North's state-run media said that Pyongyang will communicate "through visits at different level on a regular basis in the future".