United States President Donald Trump speaks during the United Nations General Assembly at U.N. headquarters, Sept. 19, 2017.
United States President Donald Trump speaks during the United Nations General Assembly at U.N. headquarters, Sept. 19, 2017.

UNITED NATIONS - U.S. President Donald Trump, in his first address to the United Nations General Assembly, doubled down on criticisms of North Korea, Iran, Cuba and Venezuela.

Trump warned North Korean leader Kim Jong Un, whom he described as "rocket man", that the United States is prepared to "totally destroy" his country if Pyongyang continues moving forward with its nuclear ambitions.
WATCH: Trump warns North Korean leader

On his favorite social media outlet Tuesday, Trump expressed anticipation as he makes the most important speech of his presidency. "Big day at the United Nations - many good things, and some tricky ones, happening," he tweeted. "We have a great team. Big speech at 10 a.m."

North Korea, Iran, Venezuela 

Those who have seen the text of his speech said Trump will call on U.N. members to confront Pyongyang over its nuclear weapons and intercontinental ballistic missile programs, and block them before North Korea's military becomes more formidable, according to administration sources.

Without citing specifics, an official briefing reporters said Trump would speak about Iran and the tension between its government's direction and policies and the desires of its people.
Trump said Monday that the United States will walk away from the Iran nuclear deal it agreed to in 2015, along with five other nations, if Washington deems the U.N.’s International Atomic Energy Agency is not tough enough in monitoring it.
The senior official, who could not be identified according to briefing rules, said Trump would also have strong words about political and economic instability in Venezuela just hours after his working dinner Monday night with Latin American presidents.

Terrorism will also be a major focus of the speech, the senior official said.

President Donald Trump makes a brief statement to
President Donald Trump makes a brief statement to the media while at U.N. headquarters in New York, Sept. 18, 2017.

UN reforms

Administration officials said Trump's General Assembly message is intended to be deeply philosophical, building on the president's remarks earlier this year in Poland and Saudi Arabia on the theme of “principled realism."
“The president spent an enormous amount of time crafting, developing and fine-tuning his address in every respect,” according to the senior White House official.
As a presidential candidate and after taking office, Trump repeatedly berated the United Nations, calling it a talking shop that is utterly weak and incompetent and “not a friend of democracy.”
At his U.N. debut Monday, he toned down his criticism substantially at an event dedicated to reforming the organization. Flanked by U.N. Ambassador Nikki Haley and Secretary General António Guterres, Trump said the United States encourages “all member states to look at ways to take bold stands at the United Nations, with an eye toward changing business as usual and not being beholden to ways of the past which were not working."

President Donald Trump shakes hands with Israeli P
President Donald Trump shakes hands with Israeli Prime Minister Benjamin Netanyahu during a meeting at the Palace Hotel during the United Nations General Assembly in New York, Sept. 18, 2017.

Meetings with foreign leaders

Trump also held one-on-one meetings with France’s President Emmanuel Macron and Israeli Prime Minister Benjamin Netanyahu, then had dinner with key Latin American leaders.

State Department Director of Policy Planning Brian Hook said both meetings had dealt primarily with Iran’s mischievous role in the greater Middle East.  

“One of the things that’s common to both the meetings, the French and the Israelis, is this deep and abiding concern about Iran’s activities in Syria; and broadly, whether it’s in Yemen, Syria, Iraq, Lebanon. One of the things they discussed was not allowing the Lebanization of Syria,” Hook told reporters.

Asked to explain the term “Lebanization”, he said, “Iran takes advantage of failed states, and civil wars, and wars generally. It is the kind of environment that is conducive to activating their proxy network, and they are doing that in Syria.

Hook said Trump repeatedly voiced concern that the two international deals signed by President Barack Obama, on Iran’s nuclear program and climate change, were unfair to the United States.

“The president focused repeatedly in [these] meetings on fairness. It was a theme he returned to again and again that he thought it [the Paris accord] was badly negotiated” Hook said. “He also thought the Iran deal was badly negotiated.”

Steve Herman at the White House and Michael Bowman on Capitol Hill contributed to this report.