A top member of Turkey's ruling AK party (AKP) has called for taking secularism out of the new constitution, arguing it is a Muslim country.
Parliamentary speaker Ismail Kahraman, who is overseeing work on the draft charter, said Turkey should have a religious constitution.
But the head of the constitutional commission said the AKP had not discussed removing secular values.
Critics fear the modern state's secular foundations are being eroded.
Opposition parties also fear the new constitution could concentrate too much power in the hands of President Recep Tayyip Erdogan, who wants an executive presidency to replace the current parliamentary system.
Turkey is a Nato member and aspires to join the EU, which has traditionally regarded the country as a model of secular democracy in the Islamic world.
The deepest faultline: analysis by Mark Lowen, BBC News, Istanbul
It is the deepest and most sensitive faultline in Turkish society - secularism versus Islamism - and the parliamentary speaker has just exposed it yet again. Since the 1920s, the Turkish constitution has disavowed a state religion.
Secularists say that allowed Turkey to be embraced by the West and that it is an untouchable cornerstone of national identity. But as the Islamists gained power under Recep Tayyip Erdogan, the balance tipped and the pious now feel today's constitution must reflect their religious identity.
In a country at one with itself, where both sides coexist peacefully, this issue could be discussed in a rational way. But Turkey is so profoundly polarised, so riven by political mistrust between supporters and opponents of the government, that the topic has sparked fear and heated debate.
One side says it is a reflection of the fact that Turkey is around 97% Muslim. The other contends it is yet another attempt by a neo-Ottoman and Islamist ruler to shape Turkey in his name. Protests have already broken out - and that is just at the suggestion of the change. If it is officially sanctioned, it would spark a huge reaction.
'Secularism cannot feature'
Speaking at a conference in Istanbul, Mr Kahraman said: "We are a Muslim country. As a consequence, we must have a religious constitution."
"Secularism cannot feature in the new constitution," he added.
Mustafa Sentop, head of the constitutional commission and also an AKP member, responded that the party had not discussed removing the precept of secularism.
The speaker had not been "speaking on behalf of his party", he was quoted as saying by AFP news agency.
The AKP, which has its Islamist roots, has been pushing to replace the existing constitution, which dates back to a 1980 military coup and does not promote any religion.
Over the past two years, the government has lifted bans on women and girls wearing headscarves in schools and civil service. It also limited alcohol sales and made efforts to ban mixed-sex dorms at state universities.
Kemal Kilicdaroglu, the head of Turkey's main CHP opposition party, condemned Mr Kahraman's comments.
"The chaos that reigns in the Middle East is the product of ways of thinking that, like you, make religion an instrument of politics," he tweeted.
"Secularism exists so everyone can practise their religion freely, Mr Kahraman!"
The government has pledged that European standards on human rights will form the basis of the new text.
The AKP holds 317 of the 550 seats in parliament. To submit its draft constitution to a referendum, it would need 330 votes , so it will need to win over lawmakers from other parties.