Joseph Yun told reporters in Bangkok that the talks could take place without preconditions and would serve Washington's dual approach of pressure and engagement on Pyongyang over its nuclear program.
Mr Tillerson added that USA communication channels remain "open" to North Korea when they want to talk.
"Our message today is one this body has heard before and one we will continue to repeat: The United States will not allow the regime in Pyongyang to hold the world hostage", Tillerson said.
"Time will tell what was the impact of our discussions, but I think we've left the door ajar", said Feltman, adding that he "fervently" hoped that "the door to a negotiated solution will now be opened wide".
"Let's see how they respond".
However, experts believe North Korea still has some technical points it needs to improve before fully completing its goal of developing a nuclear-tipped missile that can hit the entirety of the United States.
"Continuing to allow North Korean laborers to toil in slave-like conditions inside Russian Federation in exchange for wages used to fund nuclear weapons programmes calls into question Russia's dedication as a partner for peace", he said.
He said: "With respect to the talks, we are not going to accept preconditions".
In a speech in Washington on Tuesday, Tillerson said the United States will be willing to start diplomatic talks with North Korea without preconditions.
They were given several medals, including the Order of Kim Il Sung and Order of Kim Jong Il, the highest orders of the DPRK, an acronym for North Korea's official name, the Democratic People's Republic of Korea. The comment during a Q&A took White House staffers off-guard, they said.
REUTERS/Kevin Lamarque U.S. President Donald Trump and Secretary of State Rex Tillerson.
Mattis' comments came weeks after North Korea tested what it said was a new kind of ICBM capable of reaching the entire US mainland. As I said earlier this week, a sustained cessation of North Korea's threatening behavior must occur before talks can begin.
China's ambassador echoed Russia's rebukes.
"We would like to have Russia's help, very important", he continued.
He said that with crude oil still flowing into North Korean refineries, the USA also questions China's commitment to "solving an issue that has serious implications for the security of its own citizens".
It is "the most tense and risky security situation in the world today", UN Security General Antonio Guterres told the UN as the meeting opened.