The assembly approved the final 18th article of the package late on Sunday and according to parliament regulations will now take a two-day break from the talks before a second round of voting during which any changes to the articles will be debated.
The ruling AK Party, backed by the nationalist MHP, is pushing through legislation that Erdogan says will bring strong executive leadership needed to prevent a return to the fragile coalition governments of the past.
If parliament gives final approval to the constitutional package it will be put to a referendum expected in the spring, Reuters reported.
The main opposition CHP and the pro-Kurdish HDP, the second largest opposition party, strongly oppose the changes.
The reform will enable the president to issue decrees and will allow him to be a member of a political party. The plans envisage presidential and general elections in 2019 with a president eligible to serve a maximum two five-year terms.
The bill needs the support of at least 330 deputies in the 550-seat assembly to go to a referendum. The AKP has 316 deputies eligible to vote and the MHP 39.