Hosting Antonio Guterres in the Oval Office, Trump described said the pair were "friends" and embraced efforts at reform.
![Kim Jong Un has been supreme leader of North Korea since 2011 [Linh Pham/Getty Images]](data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D'http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg'%20width%3D'100'%20height%3D'100'%20data-ring-placeholder%3D'1'%3E%3C%2Fsvg%3E "Kim Jong Un has been supreme leader of North Korea since 2011 [Linh Pham/Getty Images]")
"You have done a very, very spectacular job at the United Nations," Trump said. "You need talent, and he's got the talent."
"I have to say the United Nations has tremendous potential. It hasn't been used over the years nearly as it should be," Trump said.
Trump added that he has "a feeling that things are going to happen with the United Nations that we haven't seen before."
The meeting was expected to focus on UN reform.
"I'm a true believer that we live in a messy world but we need a strong, reformed and modernized UN," Guterres said.
"We need a strong United States engaged, based on its traditional values -- freedom, democracy, human rights," he added, in what could be perceived as a barbed remark.
During Trump's maiden speech to the UN General Assembly in September, Trump distanced himself from a vision of US policy that promotes liberal values abroad.
He instead appealed for "each nation to use sovereignty as the basis for mutual cooperation.
This was the UN chief's first full formal meeting with Trump at the White House after a brief encounter with the US president in April.
During that visit to the White House, Guterres met with US national security adviser HR McMaster and dropped by the Oval Office, but there was no joint appearance with Trump.
Guterres held a bilateral meeting with Trump during the UN General Assembly session in New York last month during which the US president also led a high-level meeting on UN reform.
UN sources said they expected the Middle East peace process, North Korea, the Iran nuclear deal to be among the issues raised.
Guterres is also concerned by US threats to cut funding to the world body.
The Trump administration recently announced it was pulling out of UNESCO for alleged "anti-Israel" bias.
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