Prime Minister Binali Yildirim's government is seeking the support of Nationalist Movement Party, or MHP, for a vote in parliament that would pave the way for a referendum giving the largely ceremonial presidency full executive powers.
Opposition parties have opposed a presidential system, since they fear it would allow Erdogan to rule unchecked. But MHP leader Devlet Bahceli has switched positions and recently voiced his party's support.
Speaking after the meeting "to smooth over" differences on the proposed changes, Bahceli said the talks had been positive. The prime minister said the ruling party would be putting the final touches of a proposal that will be submitted to parliament next week with the agreement of the MHP.
The most important change envisaged, Yildirim said, is removing a constitutional requirement for the president to have no party affiliation.
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Erdogan founded the ruling Justice and Development Party, or AKP, but gave up his post as party leader last year when his term as prime minister ended and his mandate as president began.
Although he now holds a traditionally ceremonial post, Erdogan has retained outsized influence over the ruling party and the levers of government.
The proposed political changes come in the wake of a failed military coup that paved the way for a sweeping crackdown on dissent.