Volker Kauder, leader of Mrs Merkel's Christian Democrats in parliament, told a party congress he expected a "clear signal" on the issue from the Government of Prime Minister Tayyip Erdogan before membership talks could continue.
"A country that wants to be part of Europe must accept the basic principle of religious freedom," he said.
"That means we expect Christians in Turkey to be able to build churches without any restrictions, just as Muslims build mosques here in Germany."
Mr Kauder's comments were seen as more of an appeal to members of his party who are sceptical about letting a Muslim-majority country into the EU, rather than an attempt to block Turkey's membership talks
There was no immediate reaction from Ankara.