By Jeremy Diamond, CNN

(CNN) -- President Donald Trump stepped up to the iconic dais at the United Nations General Assembly on Tuesday on the heels of a year during which his presidency has shaped and shaken the world.

"Today, I stand before the United Nations General Assembly to share the extraordinary progress we've made," he began. "In less than two years, my administration has accomplished more than almost any administration in the history of our country."

There was some muted laughter from the room.

"So true," Trump said.

"I didn't expect that reaction, but that's OK," he said, prompting louder laughter.

In the year since he made his first appearance at the UN as president, Trump has sparked trade wars with allies and adversaries alike, delivered a stunning diplomatic détente with North Korea and withdrawn the United States from yet more multilateral agreements and commitments.

Those efforts will all be on display as Trump addressed the gathering of world leaders, delivering a speech that -- like last year -- touted the President's "foreign policy successes.

Ahead of the speech, officials said Trump will emphasize US commitment to its sovereignty above all international organizations and multilateral agreements on the heels of several moves that have put that effort on display, including most recently a decision to cut funding for the UN agency that supports Palestinian refugees and a speech by his national security adviser John Bolton undercutting the International Criminal Court.

Bolton, a longtime and fiercely ideological critic of the UN and the former US ambassador to the body, is certain to leave his imprint on Tuesday through Trump's speech.

"We, the people, are sovereign in America, so that infringements on our sovereignty are not infringements on abstractions or infringements on the government. They're an infringement on the people themselves," Bolton said on Monday. "And it's why we believe -- and of course, I'm speaking in secular terms here -- that the Constitution is the highest authority that we recognize. So in a number of different ways, the President's going to address this issue."

Addressing the sovereignty theme, Secretary of State Mike Pompeo also said Monday Trump will deliver "a recap about his call for every nation to do its part has paid dividends for the United States and the world over this past year."

US Ambassador to the UN Nikki Haley has also said Trump will "lay down a marker" on foreign aid, remaining generous, but only "to those that share our values ... that want to work with us."

Trump's speech also comes amid an undercurrent of global unease as Trump continues to up the ante in his trade war with China, after Trump slapped tariffs on another $200 billion in Chinese imports with promises to punch up if China retaliates, threatening to roil the global economy. Trump is expected to address the US's posture on trade -- including toward China -- and defend the tariff actions he has taken with increasing verve over the last year.

Speaking a year after he threatened to "totally destroy North Korea" if it endangered the US or its allies and dubbed the country's leader Kim Jong Un "Rocket Man," Trump will spotlight how radically circumstances have changed since then, touting his diplomatic efforts that were buttressed by international sanctions passed at the UN.

Already on Monday, Trump was quick to address the state of diplomacy with North Korea as he arrived at UN headquarters.

"This is a different world. That was a very dangerous time," Trump said. "This is one year later, a much different time."

CNN's Betsy Klein contributed to this report.