"The cumulative actions of the DPRK since their last nuclear test compel us to look at a range of measures that would apply pressure," said the spokesperson for the US mission to the United Nations.
"We are exploring options for a response to this series of provocations with our Security Council colleagues."
Diplomats had said that the United States was preparing a new sanctions resolution in the event of a further nuclear or missile test.
Yesterday, North Korea said it will carry out a nuclear test "at any time and at any location" set by its leadership, fueling fears in the region of an escalation.
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North Korea is seeking to develop a long-range missile capable of hitting the US mainland with a nuclear warhead, and has so far staged five atomic tests since 2006, two of them last year.
At the council meeting on Friday, Tillerson called on all countries to downgrade or sever diplomatic relations with North Korea and impose targeted sanctions on entities and individuals supporting its missile and nuclear program.
Washington has repeatedly called for stronger UN sanctions, but wants China, North Korea's main trading partner and ally, to toughen its approach.