US President Donald Trump addresses the 72nd United Nations General Assembly at UN headquarters in New York, US, Sept 19, 2017. [Photo/Agencies]

US President Donald Trump's 41-minute speech at the United Nations on Tuesday, particularly his saber-rattling rhetoric on Pyongyang, has aroused a strong reaction in the United States and beyond, with many believing his words exacerbate the situation on the Korean Peninsula.

In his debut at the UN General Assembly, Trump strongly pressured the Democratic People's Republic of Korea to give up its nuclear weapons and criticized a landmark Iran nuclear deal reached by his predecessor.

Trump threatened that the US "will have no choice but to totally destroy" the DPRK unless Pyongyang refrains from its nuclear tests and missile launches.

Trump's bellicose words came minutes after UN Secretary-General Antonio Guterres said at the beginning of the General Assembly meeting Tuesday morning that a solution to the DPRK must be political.

"This is a time for statesmanship," Guterres said."We must not sleepwalk our way into war."

"I think it's to be expected that the president would declare he's prepared to defend our country and our allies," said David Lampton, director of China studies at Johns Hopkins University's School of Advanced International Studies.

"But there is a saying that when everyone is losing their head, it is most important to keep your own head. … I think the words he used, and the way he used them does not make the situation better," Lampton told China Daily on Tuesday.

Mitt Romney, the former governor of Massachusetts and the 2012 Republican presidential nominee, tweeted on Tuesday that Trump gave a "strong and needed challenge" to UN members to confront global challenges.

But US Senator Dianne Feinstein, a Democrat, said Trump missed an opportunity to present any positive steps the UN could take on Pyongyang and offered no path forward on the Iran issue.

"The goals of the United Nations are to foster peace and promote global cooperation. Today, the president used it as a stage to threaten war," she said in a statement.

Swedish Foreign Minister Margot Wallstrom told Swedish national radio on Tuesday that Trump's speech was "remarkable" and contained a direct military threat, in breach of the UN charter.

In contrast to Trump's combativeness, US Defense Secretary James Mattis said hours after the president's speech that he hopes to find a diplomatic solution to the situation with the DPRK.

"We are dealing with the North Korea situation through the international process and we will continue to do so," Mattis said, according to Reuters. "Secretary Tillerson is leading the effort, and we will hopefully get this resolved through diplomatic means."

Trump offered a note of thanks to China and Russia for supporting the UN resolutions on the DPRK, but said "it is an outrage" that some nations trade with or financially support the DPRK.

Beijing has reiterated that it has done its best in implementing all the UN Security Council resolutions on the DPRK.