Erdogan, who has dominated Turkish politics for 14 years, has long pushed imbuing the presidency with greater political powers, arguing that strong leadership would help Turkey grow.
The main opposition party fears that if approved, the reforms would concentrate too much power in Erdogan's hands, turn the country into a de facto dictatorship and move Turkey away from democracy and its anchor in the West.
"They are trying to turn the democratic parliamentary regime into a totalitarian regime," main opposition leader Kemal Kilicdaroglu said.
If approved by lawmakers, the government will submit the package to a voter referendum for final approval - possibly in the spring.
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Today, police used pepper spray to disperse a group of legislators, lawyers and other protesters who tried to gather near an entrance to the parliament building to oppose the proposed constitutional changes.
Some roads leading to parliament were blocked in an apparent bid to prevent demonstrations. The ruling party, founded by Erdogan, is 14 votes short of the required 330, but has secured the backing of the country's nationalist party.
Other proposed amendments would increase the number of seats in the 550-member Parliament to 600, reduce the minimum eligibility age for legislators from 25 to 18, and set parliamentary and presidential elections on the same day.
The debate comes at a difficult time for Turkey, which has been rocked by a wave of bombings, renewed conflict with Kurdish rebels in the southeast, a military offensive in Syria and a failed coup attempt.
The government has argued a strong presidential system would reduce instability.