Kurtulmus -- a minister for the ruling Justice and Development (AK) Party -- made the remarks in Ankara after a Council of Ministers meeting.
When asked about developments in an ongoing constitution draft debate in parliament, Kurtulmus said:
"Our talks with the MHP on constitutional change continues in a clear and transparent way. The MHP will support the new constitutional draft which has already started to be debated in the parliament," he added.
Constitutional change, in particular, the call for a presidential system, has been on the political agenda since Recep Tayyip Erdogan, the former prime minister and AK Party leader, was elected Turkey's president in August 2014.
That election was the first time a Turkish president was directly chosen by popular vote.
The proposed changes would be put to a public referendum even if the government got the necessary votes in parliament to avoid the need for one, Prime Minister Binali Yildirim said last month.
Turkey's new constitutional draft needs 330 votes to pave the way for a referendum.
The AK Party, with 316 seats, and the MHP, with 40, both back the bill.