North Korean leader Kim Jong-un has sent a rare congratulatory message to Xi Jinping and US President Donald Trump called Mr Xi "a very good person" following the announcement of the Chinese leader's second five-year term.

Key points: China's Xi Jinping has just consolidated his power during the country's national congress

China's Xi Jinping has just consolidated his power during the country's national congress Mr Trump says he and Mr Xi have "the best relationship", leaders discussed North Korea issues

Mr Trump says he and Mr Xi have "the best relationship", leaders discussed North Korea issues Mr Kim said "the Chinese people have entered the road of building socialism" under Mr Xi

Mr Kim wished the Chinese President "great success" in his future, North Korean state media said.

The friendly gesture by the North Korean leader, who rarely issues personal messages, was sent at the end of China's Communist Party Congress at which Mr Xi became China's most powerful leader since Mao Zedong.

Mr Trump said he spoke to Mr Xi directly and congratulated him on his second term.

In an interview with Fox Business Network's Lou Dobbs taped shortly after the phone call, Mr Trump described Mr Xi's elevation as something that had "really virtually never happened in China".

"He's a powerful man. I happen to think he's a very good person," Mr Trump said, describing their relationship as notably strong.

"People say we have the best relationship of any President-President, because he's called President also.

"Now some people might call him the king of China. But he's called President."

The US President said the leaders discussed North Korea on the call, as tensions between the nuclear state and US allies continued to escalate.

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Mr Trump said an upcoming trip to China would be "historic and positive" with serious progress on North Korea.

The messages came as China was being urged by the international community to do more to rein in the North's missile and nuclear tests that have raised tensions globally.

Mr Trump had been one of the most vocal critics of China and its leadership during the North Korea crisis.

Mr Kim's letter "expressed the conviction that the relations between the two parties and the two countries would develop in the interests of the peoples of the two countries", the North's state-run central news agency said in a statement.

"The Chinese people have entered the road of building socialism with the Chinese characteristics in the new era" under the guidance of Mr Xi, the message said.

Mr Xi received messages from Russian Prime Minister Dimitry Medvedev, Italian President Sergio Mattarella and Cuba's Raul Castro, who said he hoped the two countries could further improve the brotherhood between their peoples and parties.

Reuters/AP