UN Secretary-General Antonio Guterres has warned world leaders against war with North Korea, calling on them to take the threat of "nuclear peril" seriously.

"We must not sleepwalk our way into war," said Guterres on Tuesday at the annual summit of the United Nations General Assembly (UNGA) in New York.

"When tensions rise, so does the chance of miscalculation. Fiery talk can lead to fatal misunderstandings," he said in his first state-of-the-world report since taking the top job at the UN on January 1.

"The solution must be political. This is a time for statesmanship."

His message on "fiery" rhetoric was implicitly directed at North Korean leader Kim Jong-un, but also at the United States and President Donald Trump, who later warned of "totally destroying North Korea" if it does not back down.

"The United States has great strength and patience, but if it is forced to defend itself or its allies, we will have no choice but to totally destroy North Korea," Trump told the UNGA, shortly after Guterres' speech.

"'Rocket Man' is on a suicide mission for himself and for his regime. The United States is ready, willing and able, but hopefully this will not be necessary," Trump added, referring to the North Korean leader with a nickname he gave last week on Twitter.

The UN Security Council has unanimously imposed nine rounds of sanctions against North Korea since 2006 and Guterres appealed for the 15-member body to maintain its unity on Pyongyang.

Rohingya, migration, climate

Guterres, a former head of the UN refugee agency, also urged the Myanmar government to end the "vicious cycle of persecution, discrimination, radicalisation and violent repression" that has seen more than 400,000 Rohingya Muslims flee into neighbouring Bangladesh.

He called for the UN and humanitarian agencies to be allowed access to Rakhine to offer aid.

Guterres also addressed the issue of global migration.

The number of refugees on the move in the world can be managed with a global sharing of responsibility, he said.

"I myself am a migrant, as are many of you. But no one expected me to risk my life on a leaky boat or cross a desert in the back of a truck to find employment outside my country of birth," Guterres said.

"Safe migration cannot be limited to the global elite."

He also spoke about the climate change, calling on the world to "get off the path of suicidal emissions".

"We know enough today to act. The science is unassailable," he said, reiterating his message to global leaders to implement the Paris Agreement "with ever greater ambition".