US President Barack Obama has offered a heartfelt tribute to Muhammad Ali as the outpouring of emotion continues following the boxing legend's death.

Ali died on Saturday aged 74 after losing his battle with a respiratory illness. He was admitted to hospital on Thursday with breathing difficulties and was later placed on a life-support machine.

Obama released a heartfelt statement paying his respects to Ali late on Saturday night, saying both he and first lady Michelle Obama were mourning the legend's passing.

"Muhammad Ali was The Greatest. Period. If you just asked him, he'd tell you. He'd tell you he was the double greatest; that he'd 'handcuffed lightning, thrown thunder into jail'," Obama said.

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"But what made The Champ the greatest - what truly separated him from everyone else - is that everyone else would tell you pretty much the same thing," the statement said.

So much a fan is President Obama that a pair of Ali's boxing gloves hangs above an iconic photograph of Ali defeating Sonny Liston of in a private Whitehouse study.

"(Ali was) a man who fought for us. He stood with King and Mandela; stood up when it was hard; spoke out when others wouldn't," President Obama said.

Obama's obituary wasn't completely sugar-coated: "For all his magic in the ring, he could be careless with his words, and full of contradictions as his faith evolved," he said.

"But his wonderful, infectious, even innocent spirit ultimately won him more fans than foes - maybe because in him, we hoped to see something of ourselves."

Here's how the world is remembering him on social media: