What you need to know:
- North Korea's main ally China has signed up to the sanctions, including restrictions on imports, as has Russia.
- Trump has previously kept the door open to possible talks with North Korea.
- It emerged on Sunday that Italy has ordered North Korea's incoming new ambassador to leave the country in a protest over Kim's missile launches and nuclear tests.
US President Donald Trump said negotiating with North Korea over its nuclear program would be a waste of time Sunday after it emerged that Washington had channels of contact with Pyongyang.
Only hours after his Secretary of State Rex Tillerson revealed that US officials were in touch with North Korean counterparts, Trump undercut his top diplomat by declaring on Twitter that any talks would be futile.
"I told Rex Tillerson, our wonderful Secretary of State, that he is wasting his time trying to negotiate with Little Rocket Man," he said, referring to North Korean leader Kim Jong-Un.
"Save your energy Rex, we'll do what has to be done!"
Speaking on Saturday after talks with China's President Xi Jinping, Tillerson said that US officials had "two or three" channels of communication with North Korea despite an escalating war of words between their respective leaders.
Asked how he could know whether the North would even contemplate coming to the table, Tillerson told reporters in Beijing: "We are probing, so stay tuned."
"We have lines of communication with Pyongyang. We're not in a dark situation, a blackout, we have a couple, three channels open to Pyongyang."
"We can talk to them, we do talk to them," he said.
But the State Department later said in a statement that North Korea "have shown no indication that they are interested in or are ready for talks regarding denuclearization."
And on Sunday afternoon the department's spokeswoman Heather Nauert issued her own tweets in what appeared to be an attempt to harmonize the mixed messages.
"#DPRK will not obtain a nuclear capability. Whether through diplomacy or force is up to the regime @StateDept," she wrote, before tagging the president in her second message: "Diplomatic channels are open for #KimJongUn for now. They won't be open forever @StateDept @potus."
In a recent speech at the United Nations General Assembly, Trump threatened to "totally destroy" North Korea in the event of an attack on the US or any of its allies, deriding Kim as a "Rocket Man" who was on a "suicide mission."
Kim responded by calling Trump a "mentally deranged dotard."
His administration has also been at the forefront of a drive to impose a series of sanctions against North Korea in response to its sixth nuclear test — the largest yet — and the firing of two missiles over Japan.
North Korea's main ally China has signed up to the sanctions, including restrictions on imports, as has Russia.
But, uneasy over Trump's bellicose tone, both countries have appealed to the US to have talks with North Korea, and Tillerson's revelation was welcomed on Sunday by Germany.
"This is exactly the right course and a courageous step," German Foreign Minister Sigmar Gabriel said in a statement.
"North Korea would be well advised to take this offer of talks seriously."
Gabriel also urged the US to have dialogue with Iran over a nuclear accord which Trump appears on the verge of scrapping, adding that such a move "would undermine the credibility of the offer to North Korea."
Trump has previously kept the door open to possible talks with North Korea.
In a meeting with Japanese Prime Minister Shinzo Abe and South Korean President Moon Jae-in on the sidelines of the UN, Trump responded "Why not?" when asked whether there could be talks.
But his administration has also been urging allies to ratchet up the pressure on Kim's regime by isolating it diplomatically.
It emerged on Sunday that Italy has ordered North Korea's incoming new ambassador to leave the country in a protest over Kim's missile launches and nuclear tests.
"We have taken the firm decision to interrupt the accreditation procedure. The ambassador will have to leave the country," Foreign Minister Angelino Alfano said in an interview with Italian daily La Repubblica.
"We want to make Pyongyang understand that isolation is inevitable if it does not change course."