Erdogan has repeatedly threatened in the past 18 months to begin an offensive against the US-backed Kurdish YPG militia east of the Euphrates River after two previous operations in the war-torn country in 2016 and 2018.
But the threats never came to fruition after the United States proposed forming a "safe zone" earlier this year in a bid to stop any Turkish intervention.
Syria at peace talks says ceasefire depends on Turkey
"We entered Afrin, Jarabulus and Al-Bab. We will go into the east of the Euphrates next," Erdogan said, referring to areas captured by Turkish-backed Syrian rebels.
"We have told Russia and America this. Because for as long as we are subject to harassment, it is not possible for us to stay silent," Erdogan said during a televised speech in the northwestern city of Bursa.
"We can only be patient for so long. That patience will come to an end," he added.
Ankara has in the past year reported incidents of Turkish soldiers coming under fire from the YPG in northern Syria.
Erdogan's threat came a day before a US military delegation holds talks in Ankara with Turkish officials on the "safe zone".
Ankara says the People's Protection Units (YPG) militia is a "terrorist offshoot" of Kurdish militants waging an insurgency inside Turkey since 1984.
But the US has worked closely with the YPG against the Islamic State (IS) group.
US President Donald Trump proposed setting up a 30-kilometre "safe zone" along the border after Erdogan threatened to enter Syria in December.
Turkish officials have said any "safe zone" should be under Ankara's control and that all YPG elements must be removed from the region.
Turkish foreign ministry spokesperson Hami Aksoy on Friday said there was still no agreement on the "safe zone" as Ankara expected the US to bring new proposals.
Damascus rejects Turkey-US talks on Syria buffer zone
He said that if no "common ground was reached with the US", Turkey would be forced to "set up the safe zone by ourselves".
In the past couple of weeks, there have been reports in local media of military vehicles and commando units being sent to Turkish towns on the border with Syria.
Turkish forces supported Syrian rebels in a 2016 operation against IS, while early in 2018, Ankara-backed opposition fighters captured Afrin from the YPG.
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