March 29, 2017 0313 GMT
The new constitution, which would replace the basic law drawn up after Turkey's 1980 military coup, seeks to establish for the first time a presidential system for ruling the modern republic created from the ashes of the Ottoman Empire, AFP wrote.
Critics have claimed the move is part of a power grab by Erdogan – Turkey's premier from 2003-2014 and then president – for one-man rule in the wake of the failed coup in July.
But Erdogan and the ruling Justice and Development Party (AKP) say the presidential system would bring Turkey into line with countries such as France and the United States and is needed for efficient government.
The debates on the 18-article new constitution began after the draft was agreed by a parliamentary commission. The two readings are expected to last 13-15 days.
A group of protesters rallied outside the parliament building in Ankara ahead of the debate, but police broke up the gathering using pepper spray on the demonstrators.
The AKP needs more than 330 votes – a three fifths majority – for the bill to be submitted to a referendum for voters' approval.
However, the November 2015 election left the AKP short of a super majority in parliament and it is relying on the support of the opposition right-wing Nationalist Movement Party (MHP), the fourth largest in the legislature.
Once approved by parliament, a referendum is expected to take place within 60 days, indicating a date in late March or early April.
Pro-government newspapers have predicted a thumping victory for the ruling party although other commentators have been more cautious.
The new constitution is opposed by the biggest opposition party, the Republican People's Party (CHP), whose deputy chairman Bulent Tezcan said it would restore powers "to the palace" taken away from the Ottoman Sultan a century ago.
"It will be the dissolution of all that our republic has achieved," he said, criticizing the draft as paving the way for "one man dictatorship".
But AKP lawmaker Halil Firat, who helped draw up the proposed new constitution, said it would make clear the roles of government and president.
"Stability will be achieved. Decision-making will be quick."
Under the proposed new constitution, the president would not have to sever links with a political party, as is the case now even though Erdogan co-founded the AKP.
It is also expected to lead to the creation of the posts of vice presidents and the abolition of the office of prime minister.
There would no longer be a formal cabinet but there will be ministers. The president will have the power to appoint and fire ministers.
The draft law says the president would be elected for a five-year term and serve for a maximum of two mandates.
If Erdogan's existing time as president is not counted, it would mean in theory he could stay in office until 2029, with the next elections due in 2019.
Parliamentary elections would be held every five years – not four as at present – and on the same day as presidential polls. Both elections would be scheduled to take place on November 3, 2019.