Cheong Wa Dae officials earlier said Moon and Trump will be joined by Japanese Prime Minister Shinzo Abe in NY for a three-way summit.
Meanwhile, North Korea has said it wants "equilibrium" with the U.S.
The remarks also came after H R McMaster, the US' National Security Adviser, reaffirmed that the Trump administration has military options in place for dealing with North Korea.
Pyongyang says it needs nuclear weapons to protect itself from "hostile" United States forces and is determined to build a weapons system capable of delivering a nuclear warhead to hit the U.S. mainland.
7 killed in remote-controlled explosion in Bajaur Agency
Pakistani Army have launched a massive search operation in the area to nab the blast executors and have cordoned the area. A senior official died in the blast along with five others.
Trump has said the USA and its allies will not be intimidated by the reclusive nation. "We will defend our people, our nations, and our civilization, from all who dare to threaten our way of life".
"This includes the regime of North Korea, which has one again shown its utter contempt for its neighbours, and the entire world community", Trump added. "Now it is not what we would prefer to do".
They agreed to continue their discussions when they meet in NY for the U.N. General Assembly later this week, according to the spokesman.
"These sanctions are just now taking effect", he said, without providing evidence. "And at that point there is not a whole lot the security council is going to be able to do from here when you have cut 90% of the trade and 30% of the oil", she said.
Zoetis' (ZTS) "Buy" Rating Reiterated at Cantor Fitzgerald
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Former top White House aide Steve Bannon told a reporter in August that there are no military solutions for North Korea. A new set of United Nations sanctions that even Trump declared a "small step", extensive talks and a rhetorical two-step that leaves them where they have been for years.
Mattis agreed, saying at the time that "there are strong military consequences if the DPRK initiates hostilities".
North Korea has launched dozens of missiles under Kim's leadership as it accelerates a weapons program created to give it the ability to target the United States with a powerful, nuclear-tipped missile.
"I believe it will further North Korea's isolation - diplomatic and economic isolation - because more and more nations are realising there's simply no collaboration with the global community".
Temer chama aliados e advogados para discutir nova denúncia de Janot
A possibilidade de 1 pronunciamento em cadeia nacional foi aventada durante uma reunião realizada ontem (15.set) em São Paulo. Na equipe do Palácio do Planalto, auxiliares que defendiam que o presidente fizesse um pronunciamento.
"The two leaders agreed to further strengthen the close cooperation between South Korea and the United States, and put more practical pressure on North Korea based on their cooperation to make North Korea realize it will only become more isolated diplomatically and face additional economic pressure if it continues to make provocations and eventually enter the path of collapse", Park said of the telephone conversation between Moon and Trump held earlier in the day. But the North American Aerospace Defence Command (NORAD) had said the ballistic missile did not pose a threat to North America.