White House press secretary Sarah Sanders said the only exception would be talks aimed at bringing home Americans detained by North Korea.
"There is a difference between talking and putting diplomatic pressure and we strongly support putting diplomatic pressure on North Korea which we're continuing to do. But now is not the time simply to have conversations with North Korea," she said.
Tillerson revealed Sunday that US officials are in exploratory contact with their North Korean counterparts, despite an escalating war of words between the two countries' leaders over Pyongyang's missile and nuclear programs.
President Donald Trump undercut his top diplomat hours later, saying that negotiating with North Korea over its nuclear program would be a waste of time.
The State Department later clarified that North Korea has "shown no indication that they are interested in or are ready for talks regarding denuclearization."
In a recent speech at the United Nations General Assembly, Trump threatened to "totally destroy" North Korea if it threatens the US or any of its allies, deriding Kim as "Rocket Man" and warning he is on a "suicide mission."
Kim responded by calling Trump a "mentally deranged dotard."
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