Erdogan, who won Turkey's first direct presidential election in August 2014, said a head of state elected by the people should have more than a symbolic role. Previously parliament had picked Turkey's president, as reported by Reuters.
The current situation, in which both the prime minister and president are popularly elected, is unsustainable, Erdogan said in a speech to civil society groups.
"In building the "New Turkey," we think Turkey needs an executive presidential system and a new constitution. This discussion should not be presented as a matter of my personal ambition," he told a packed conference hall.
"If the presidential system is the right choice for Turkey's future then it should be put into practice," he said.
Erdogan served as prime minister for more than a decade and ran for the presidency in 2014 in the expectation of swift constitutional reform that would grant the head of state new executive powers.
But his plans have been impeded in part because of opposition fears of what they regard as an increasingly authoritarian style.
Opposition parties agree on the need to replace the current constitution, born of a 1980 army coup and still bearing the stamp of its military authors, in a country which is a candidate for European Union membership. But they oppose the plans to entirely overhaul what is now a largely ceremonial presidency.
Erdogan said he expected political parties and civil society groups to take part in forging a new constitution and that the separation of powers would be one of the main points of debate.
The people, not parliament, should ultimately decide on the new text, he said, signaling the likelihood of a referendum.