Trump signaled ahead of the meeting that new sanctions would be announced against North Korea.
"Finding a fundamental way to end this vicious circle of provocations and sanctions is the most important task confronting the United Nations", he said, reminding the audience of the UN's inception after World War II as a means to prevent another destructive conflict.
The rhetorical battle came as outside experts say North Korea is getting closer to achieve its long-stated goal of building nuclear-armed missiles capable hitting anywhere in the US mainland.
The new set of USA sanctions on financial institutions that do business with North Korea is not targeted specifically at China, Treasury Secretary Steve Mnuchin said Thursday.
"This action is directed at everyone", Mnuchin said, adding the steps are "in no way specifically directed at China".
Despite North Korea's "flagrant violations", the South Korean government and the global community are making every effort to resolve the situation peacefully, he said.
The step would amount to major progress in U.S. efforts to cut off support for Pyongyang as punishment for its nuclear provocations. The move, which runs contrary to American and Japanese calls for an increase in economic and diplomatic pressure, marks a resumption in South Korean aid after a break of nearly two years. The executive order Trump signed Thursday will allow the Treasury Department to more aggressively target those doing business with what Trump called a "criminal rogue regime".
In his United Nations address, Abe said the world had already tried to reach a negotiated settlement with North Korea, starting with the US-backed 1994 Agreed Framework that collapsed a decade later.
North Korea conducted its sixth nuclear test this month.
"I hope North Korea will be able to choose a path of peace on one's own volition".
Mr Trump said on Thursday the USA will impose additional sanctions over the communist country's nuclear weapons build-up.
The remark indicated fresh openness for talks with Pyongyang, despite his insistence earlier this month that "talking is not the answer". China is North Korea's main trading partner and conduit for worldwide transactions.
The stand-off over North Korea's weapons development has intensified as its autocratic leader Kim Jong Un has accelerated his nation's development of a nuclear-tipped missile that could soon strike the continental United States.
During talks Thursday with Prime Minister Shinzo Abe of Japan and President Moon Jae-in of South Korea, Trump was expected to reiterate that military options are available in retaliation for North Korean threats.
That's likely to draw a rebuke from Moon, who has ruled out military action and issued warnings on the ramped-up rhetoric coming from Washington.
The United Nations Security Council votes at a meeting on threats to worldwide peace and security September 21, 2017 at the United States Mission in NY.
Trump kidded Moon about his use (or his interpreter's use) of the word "deplorable".
Trump on Thursday praised China's president Xi Jinping for the "very bold move".
Another US ally, Japan, said pressure, not dialogue, was needed. "So that was a great thing he did today". "And we also would like to thank President Xi of China".