The most recent United Nations sanctions resolution, a response to the North's successful test of a suspected hydrogen bomb, fell short of America's demand for a full oil embargo, but the new sanctions do cap oil imports.
"We hear about them every day in the news, we're all aware of that, and I think given our proximity, given our partners, it does increase our urgency".
A U.S. military strike had about a 25 per cent possibility, Mr Rudd said. One critic tells VOA that Pyongyang will divert at least 30% of food aid "to the military or the elite".
Cho Myung-gyon, South Korea's unification minister, said the government had "consistently said we would pursue humanitarian aid for North Korea in consideration of the poor conditions there among children and pregnant women".
Moon came to power in May on a platform of more engagement with North Korea.
Following his speech at the UN, South Korean President Moon Jae-in will meet with his US counterpart to discuss North Korea's nuclear crisis amid escalating tensions over whether President Donald Trump's harsh rhetoric against North Korean leader Kim Jong-un could lead to a miscalculation.
President Trump concludes combative United Nations address
He strongly hinted that his administration would soon back out of the deal with Iran's "murderous regime". He asked other countries to shoulder more responsibility in maintaining global peace and prosperity.
Moon is scheduled to meet with US President Donald Trump and Japanese Prime Minister Shinzo Abe on the sidelines of the United Nations meeting later Thursday.
Russian Foreign Minister Sergey Lavrov reacted to Trump's speech by saying threats will not help solve the North Korean missile problem.
But two senior South Korean diplomats, interviewed by Reuters, expressed concern that Trump's rhetoric could provoke a miscalculation from Kim and prompt him to launch an attack. "The danger is that North Korea's physicists are working to an altogether different and faster timetable than the NY diplomats". USA nuclear weapons were withdrawn from the Korean peninsula in the early 1990s at the close of the Cold War.
Mr Trump previously warned that "all options" were on the table and that North Korea would face "fire and fury" if it continued to threaten the US.
"The situation surrounding the North Korean nuclear issue needs to be managed stably so that tensions will not become overly intensified or accidental military clashes will not destroy peace", Moon said. The missile was launched on a normal trajectory, not in a "lofted" style.
The fresh measures followed the sixth and most powerful nuclear test conducted by Pyongyang earlier this month.
U.S. President Donald Trump (R) and South Korean President Moon Jae-in depart after delivering a joint statement from the Rose Garden of the White House in Washington, U.S., June 30, 2017. The UN Security Council unanimously passed new sanctions against North Korea in the wake of that test.