The Turkish government says it is "out of the question" for it to hand over a revered medieval church where Catholics want to hold Christian services.
The church, currently run as a museum, stands in the south-eastern town of Tarsus, where St Paul was born.
The Turkish constitution guarantees freedom of religion, but Christian groups in the country believe that in practice they face discrimination.
Next week the Vatican will hold a Catholic-Muslim forum to improve ties.
It was the Cardinal Archbishop of Cologne in Germany who first challenged the Turkish government to hand over the church in Tarsus.
He has pointed out that Muslims of Turkish origin in Germany are free to worship and build new mosques, but that Christians in Turkey face substantial obstacles to their religious freedom.
The Turkish government's response to the BBC leaves no room for doubt about its intention to retain control of the church.