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The United Nations is consumed with bureaucracy and not living up to its potential, US President Donald Trump said on Monday, during his debut speech its headquarter's in New York.

"Focus more on people, less on bureaucracy," said Trump, the long-time critic of the UN.

He said the cost of running the UN should be shared out proportionately among member states - referring to the US' covering a whopping 28.5 percent of the body's overall peacekeeping bill.

The president's criticism was balanced with praise for UN Secretary-General Antionio Guterres and his reform plans.

Guterres appeared to agree with the US president's criticism, saying that excessive red tape held back the international body.

"Someone out to undermine the UN could not have come up with a better way to do it than by imposing some of the rules we have created ourselves," Guterres said.

Trump's inaugural speech to the UN is due to be followed by a longer speech on Tuesday, when the US leader is expected to call for a tougher stance on Iran and North Korea. 

His words on Monday reflected a more measured approach to the United Nations, which he had previously described as "just a club for people to get together, talk and have a good time".

In exiting the meeting, Trump rounded off his message on a lighter note, harking back to the campaign slogan of his 2016 presidential bid.

"I think the main message is 'Make the United Nations Great,;" said Trump, referencing his "Make America Great Again" slogan. "Not again. 'Make the United Nations Great,'" he added.