ISTANBUL — With his triumphant tour of the countries of the Arab Spring this month, Prime Minister Recep Tayyip Erdogan has managed to set up Turkey on the international stage as a role model for a secular democracy in a Muslim country — as, in his words, “a secular state where all religions are equal.”

The only trouble is that he has yet to make that happen for Turkey.

The relationship between religion and the state, ever the sore spot of Turkish identity, is one of the most explosive issues of the debate on the new constitution that Mr. Erdogan has pledged to give the country in the new legislative term that opens Saturday.

That debate will have to deal with the elephant in the room: the total control that the state exerts over Islam through its Religious Affairs Department, and the lack of a legal status for all other religions in a predominantly Sunni Muslim society.

“Turkey may look like a secular state on paper, but in terms of international law it is actually a Sunni Islamic state,” Izzettin Dogan, a leader of the country’s Alevi minority, charged at a joint press conference with leaders of several other minority faiths last week in Istanbul.