Erdogan to fall short of first-round presidential victory: poll
His ruling AK party is also projected to lose its parliamentary majority after the polls close.
Turkey had been due for an election next year, but Erdogan in April called for snap elections.
Gezici's survey showed Erdogan receiving 48.7 percent of votes in the first round, with closest rival Muharrem Ince garnering 25.8 percent. The Iyi Party's Meral Aksener followed behind with 14.4 percent and the jailed pro-Kurdish HDP's Selahattin Dermitas after that with 10.1 percent.
Erdogan and his conservative AK party have ruled Turkey for more than 15 years, including its current parliamentary majority.
Their rivals the Kemalist CHP, Iyi Party and Saadet Party alliance are projected to capture 38.9 percent of the vote later this month.
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Whether the HDP receives 10 percent of the vote is crucial to the election outcome, as parties which don't meet the threshold don't enter parliament.
That rule would benefit Erdogan's AK party, which commands considerable support in the Kurdish east and southeast where the HDP is popular.
"According to the poll, the ruling party is seen losing the parliamentary majority. Despite the alliances that will be in parliament after the June 24 elections, no single party or alliance is seen reaching a simple majority," the poll said.
The June elections mark Turkey's switch to a presidential system that will strengthen the executive branch. Critics say it will lead to strongman rule in the country.
The widening crackdown in Turkey, along with deteriorating economic conditions, have shifted popular opinion away from Erdogan and his ruling party.
"These general and presidential elections will be the most difficult elections in Turkey's past 20 years," Gezici said.
Agencies contributed to this report.