In a tweet over the weekend, Trump referred to North Korea's leader as "Rocket Man" - an apparent reference to the country's recent repeated missile tests.
Trump and U.N. Secretary-General Antonio Guterres will speak at the meeting.
In spite his skepticism about the value of worldwide organisations and the United Nations in particular, Trump will seek support for tough measures against North Korea, while pressing his "America First" message to the world body.
Trump's saber-rattling rhetoric was in contrast to the comments of some of his own Cabinet members who have stated their preference for a diplomatic solution.
Macron will reportedly try to persuade Trump to keep the U.S.in the Iran deal.
He also criticised the Cuban government.
President Trump will specifically call out Iran and North Korea, making the argument that their governments are acting outside of their people's self-interest.
"If this is not twisted enough, now North Korea's reckless pursuit of missiles and nuclear weapons threatens the entire world", Mr Trump said.
Using bellicose language rare for an USA president at the rostrum of the United Nations, Trump touched upon hot spots around the globe, declaring "The scourge of our planet is a group of rogue regimes".
- The nuclear deal with Iran is "one of the worst and most one-sided transactions the United States has ever entered into".
"I think the main message is 'Make the United Nations Great.' Not again". It pays 25 percent of the U.N.'s regular operating budget and over 28 percent of the separate peacekeeping budget - a level of spending that Trump has complained is unfair.
The administration has framed those speeches as moments of triumph for Trump, in which he's been able to effectively transmit the "America First" vision, which electrified his campaign crowds, to foreign audiences wary over years of American interventionism.
The President said he will put United States first and ask all the leaders to put their countries first. "Over and over, he stressed the rights and roles of "strong, sovereign nations" even as they band together at the United Nations". He has pulled the Unites States out of multinational agreements, considered shrinking the US military footprint in the world and deployed bombastic language on North Korea that has been criticized by other world leaders.
Trump called the collapsing situation in Venezuela "completely unacceptable" and said the United States can not stand by and watch.
He said that the USA was "ready, willing and able" to take military action, but said hopefully that would be unnecessary, if the rest of the world stepped up its efforts to constrain the Pyongyang regime.
Guterres said that efforts were needed to change "fragmented structures" and "byzantine procedures" in the United Nations, making it a more "nimble and effective, flexible and efficient" global organization.
Ri is due to address the General Assembly on Friday.
"We are all shocked by the dramatic escalation of sectarian tensions in Myanmar's Rakhine state", said Guterres.
While North Korea has topped the national security agenda due to its repeated nuclear tests, the inclusion of Iran in this rogue axis is certain to generate discussion among the worldwide community, which remains heavily divided on the best way to confront Iran while upholding the Obama administration's landmark nuclear deal.