Recep Tayyip Erdogan had specially flown to Louisville in the southern US state of Kentucky to say farewell to Ali, who the Turkish president is known to have admired hugely as a committed Muslim and civil rights campaigner.
Erdogan on Thursday attended a prayer ceremony for Ali and had been due to attend the funeral on Friday along with several other high profile political leaders.
Thousands gather for Muslim funeral honouring Muhammad Ali
But the president's office said that Erdogan left the United States for Turkey late Thursday after attending the prayer ceremony and joining a Ramadan fast-breaking dinner with the US diaspora of Meskhetian Turks who were expelled from their homeland by Stalin in the 1940s.
The Dogan news agency quoted presidential sources as saying funeral organisers refused to allow Erdogan to lay a cloth from the Kaaba on Ali's coffin during the ceremony.
Erdogan and the Sunni cleric who heads Turkey's religious affairs agency, Mehmet Gormez, had also wanted to give readings from the Quran but were not allowed to, it added.
Have 'at least 3 kids', Erdogan tells Turkish women
The Turkish president's bodyguards and US Secret Service agents also clashed briefly while he was in Louisville.
During his trip, Erdogan was full of praise for Ali, hailing him as a fighter not just in the ring but for Muslims in general.
"While running from success to success in the rings, he also became the voice of the oppressed and victims along with Muslims from every corner of the world," he said.
Erdogan's lightning visit to the US also caused consternation in Turkey, with Erdogan leaving the day after a bomb attack in Istanbul claimed by Kurdish militants that killed 11 people.
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