ISTANBUL—Turkey’s government submitted a bill Saturday to overhaul the constitution and concentrate power in President Recep Tayyip Erdogan’s office, a controversial move that risks further destabilizing the country amid myriad security and economic threats.

The bill includes measures that would call for Turkey’s president to run his own cabinet and acquire executive powers currently vested in the parliamentary government. The changes give the head of state sweeping powers to govern by decree, and could potentially allow Mr. Erdogan to rule for two, five-year terms until 2029, the draft legislation shows.

The passage of the bill would send these amendments to a national referendum that would likely be held in late spring or summer. The changes pertaining to Turkey’s governance, if accepted, would go into effect in 2019.

“God willing, this will be the start of a new era,” Mr. Erdogan said during a rally in Istanbul shortly before his party introduced the bill in Ankara. “Are you ready for all of this,” the president asked a crowd of flag waving supporters, who responded with a resounding “yes.”

The 21-article legislation follows two months of secretive negotiations during a state of emergency between the ruling Justice and Development Party—known as AKP and founded by Mr. Erdogan—and the opposition Nationalist Movement Party, or MHP.