Ertegun — who counted Ray Charles, Aretha Franklin and the Rolling Stones among the stars signed to his label — died on Dec. 14 at age 83, days after falling and suffering a head injury at a Rolling Stones concert in New York City. He later slipped into a coma.
The Turkish-born Ertegun was buried at an ancestral family site near a Muslim religious lodge on the Asian side of the city following a religious service.
Gul praised Ertegun as a man who had done much to promote Turkey's image.
"Nobody has, or ever will, do what he did for Turkey in the United States," Gul said. "He has left a large void."
"The one thing he loved more than music was Turkey," the state-run Anatolia news agency quoted Lyor Cohen, chief executive of Warner Music Group, as saying.
Kid Rock said: "I have met many people, been to many places and seen many things, but he was definitely the best," according to Anatolia.
"He could not sing but he was music personified," the agency quoted the singer as saying.
A memorial for Ertegun will be held in New York early next year.
Ertegun, the son of a Turkish ambassador, started collecting records for fun but eventually became one of the music industry's most powerful figures with Atlantic, which he co-founded in 1947.
The label made its name with rhythm and blues by Charles and Big Joe Turner, but later diversified, making Franklin the queen of soul as well as carrying the banner of British rock with the Rolling Stones, Cream and Led Zeppelin, and American pop with Sonny and Cher, and Crosby, Stills, Nash & Young.