While critics say the move is part of a grab by Erdogan for one-man rule, supporters say it will simply put Turkey in line with France and the United States and is needed for efficient government.
The current constitution was adopted in 1982 after the 1980 military coup.
Erdogan has denounced as "lies" claims by opponents that parliament would be neutralised and the judiciary would come under his political authority.
What would change under the proposed 18-article constitution for the nation of 79 million people?
More powers for Erdogan
Under the new constitution, the president would have strengthened executive powers to directly appoint top public officials including ministers.
The president would also be able to assign one or several vice presidents. The office and position of prime minister, currently held by Binali Yildirim, would be scrapped.
The changes would implement a shake-up in the judiciary, which Erdogan has accused of being influenced by supporters of his ally-turned-foe, the Pennsylvania-based Islamic preacher Fethullah Gulen.
Gulen is blamed for the July failed coup but denies the government's accusations.
The president and parliament would together be able to choose four members of the Supreme Board of Judges and Prosecutors (HSYK), a key judicial council that appoints and removes personnel in the judiciary.
Parliament would choose seven members on its own in what would be renamed the Board of Judges and Prosecutors (HSK).
Military courts, which have convicted officers and even sentenced former prime minister Adnan Menderes to death following the 1960 coup, would in the future not be allowed.
Longer state of emergency
Under the proposed constitution, a state of emergency would be imposed in the event of an "uprising against the homeland" or "acts of violence which put the nation in... danger of being divided".
The president would decide whether or not to impose a state of emergency and then present it to the parliament.
Initially the emergency would last six months -- as opposed to three now -- then it could be extended by parliament after a presidential request for four months at a time.
Turkey has twice extended the current state of emergency imposed after the failed July 15 coup.
Erdogan can rejoin AKP
The number of members of the Turkish parliament would rise from 550 to 600. The minimum age limit for MPs would also be lowered from 25 to 18.
Legislative elections would take place once every five years -- instead of four -- and on the same day as the presidential elections.
The parliament would still have power to enact, modify and remove legislation. If the president were accused or suspected of a crime, then parliament could request an investigation.
The president will also have to be a Turkish citizen at least 40 years old, and can be a member of a political party.
Currently the president must be impartial and without party favour, although opponents have accused Erdogan of blatantly flouting this.
The change would again allow Erdogan to become leader of the ruling Justice and Development Party (AKP) that he co-founded.
Erdogan in power to 2029?
Erdogan was elected president in August 2014 after over a decade as prime minister, in the first ever direct elections for a Turkish head of state.
The proposed constitution states that the next presidential and parliamentary elections are to be held simultaneously on November 3, 2019.
If he won, the president would have a five-year term with a maximum of two mandates.
So the changes would mean that Erdogan could stay in power for another two terms until 2029.
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