At the meal, by no means a routine practice for USA presidents, Mr Trump talked of the organisation's "tremendous potential" and said he saw "fantastic things ahead for the United Nations". "We are not seeing the results in line with this investment".
Trump will participate in a forum on Monday with the U.N.'s senior leadership and the leaders of more than 120 other nations to discuss "Reforming the United Nations: Management, Security, and Development".
"Because his scripted voice is so different from his unfiltered voice, I think that a speech that sounds too polished would be picked apart as: is that actually what the president really thinks?"
The annual gathering of world leaders will open amid serious concerns about Trump's priorities, including his policy of "America First", his support for the United Nations and a series of global crises.
"I think he does believe the United Nations can be a very important instrument of addressing these threats to the world but I think he also takes the view that the United Nations has fallen short and he wants to motivate them in that regard", said Secretary of State Rex Tillerson.
The Security Council has discussed the matter twice in as many weeks.
A week ago, the 15-member UN Security Council unanimously adopted its ninth sanctions resolution since 2006 over North Korea's nuclear and ballistic missile programmes. We are deeply grateful he has taken the time to be with us today.More news: Interesting Facts About Sardar Sarovar Dam That Every Indian Ought To Know!
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The president on Monday praised U.N. Secretary-General Antonio Guterres, who said he shared Trump's vision for a less-wasteful U.N. that will "live up to its full potential". The U.S. has asked member nations to sign a declaration on U.N. reforms, and more than 100 have done so.
That's why it was little surprise that of the half-dozen officials from various United Nations member countries who were approached for this article in NY, none was prepared to talk on the record about the expectations for Trump's maiden speech at the General Assembly.
Trump will also have a working dinner with Latin American leaders that will touch on the crisis in Venezuela.
He is slated to meet with the Palestinians in the coming days.
Mr. Trump may also face some uncomfortable moments over his sharp criticism of the Iran nuclear deal.
Shredding the "bad deal" that curbs Iran's nuclear program could burnish Trump's hard-charging businessman brand, but would infuriate European allies and risks setting loose the dogs of war across the Middle East.
Trump arrived at the United Nations a few months after announcing that he was withdrawing the USA from an global climate agreement - negotiated during the Obama administration and signed by almost 200 countries - and amid speculation that he might be softening his position. We can not guarantee that it is suitable for the visually or hearing impaired.