Kutino Fernando set fire to what appeared to be the Muslim holy text in front of a packed congregation at the Victory Army Church in the capital, Kinshasa.
"If the report is confirmed, that would be blasphemous" said El Hadj Mudilo wa Malemba, a senior Islamic religious leader.
A general assembly of imams has demanded that the government should punish the priest for violating Islam.
They are planning a march through Kinshasa and have threatened court action.
Denial
Mr Fernando has denied the book was the Koran.
He said it was a small booklet containing handwritten Muslim prayers which he destroyed as he carried out a ceremony during which a child was converting from Islam to Roman Catholicism.
"I am amazed by the reaction," he said.
Mr Fernando, who is well known for his jewellery and designer clothing, has his own private television station and draws huge crowds to his Sunday prayer meetings.
Muslims are in the minority in the Democratic Republic of Congo, where almost half the population is Christian.
Country profiles
Koran misprint sparks Kuwaiti crisis
(04 May 99 | Middle East)
Images of Islam
(21 Jan 99 | Archive)
Should Islam allow more free speech? Your reaction
(25 Sep 98 | Talking Point)
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