The US-Turkey deal for a safe zone agreed earlier this month is intended to manage tensions between Turkey and US-backed Kurdish forces over the border in war-torn Syria that Ankara brands terrorists.
"We do not have too much time or patience regarding the safe zone. Within a few weeks if our soldiers do not start to actually control this area, there will be no other option left but to implement our own operation plans," Erdogan said during a speech in Istanbul.
Erdogan previously said US President Donald Trump had promised the "safe zone" would be 32-kilometre wide.
A joint operations centre has been set up and joint patrols are expected to start soon.
Since last year, Erdogan has repeatedly threatened to launch an assault east of the Euphrates river against the YPG, which fought against the Islamic State (IS) group.
Ankara says the Kurdish People's Protection Units (YPG) militia is a "terrorist" offshoot of the outlawed Kurdistan Workers' Party (PKK).
The PKK, which has waged an insurgency against the Turkish state since 1984, is blacklisted as a terrorist group by Ankara, the US and the European Union.
Turkey previously conducted cross-border operations in northern Syria supporting Syrian rebels in 2016 against IS and in early 2018 against the YPG.
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