The U.S. has provided air cover and other support to Kurdish forces battling the Islamic State group.
It said that Turkey had pressed ahead with the air strikes despite U.S. objections and this "should serve as a warning for what could lie in store".
Last week, Turkish airstrikes targeted Kurdish PKK forces in northern Iraq and Syria, resulting in 70 deaths, and incensing the U.S.
Mr Erdogan is due to meet president Donald Trump on May 16 in the USA, the two men's first face-to-face summit since the American leader took office in January.
For weeks rebel fighters, backed up by USA forces, have fought to try and take control of the city and its dam.
Turkey, however, considers the YPG a terrorist organization, the Syrian branch of its long-time enemy, the armed Kurdish Workers Party or PKK.
But Washington views YPG as its most effective ground partner in the fight against Islamic State of Iraq and the Levant (ISIL) in Syria.
"Coalition forces are conducting joint patrols along the northeastern Syria-Turkey border to assess reports from both the [Kurdish] SDF and Turkey regarding skirmishes and cross-border fires between their respective security forces", an official from the Combined Joint Task Force - Operation Inherent Resolve (CJTF-OIR) Public Affairs Office told RT via email, confirming the deployment.
Turkish officials announced the conclusion of Euphrates Shield in March but have said they would continue combatting terror to make its borders safe, pointing to both the Islamic State group and Kurdish militants. They are no more PKK than we are, and any attempt to equate us with the PKK is disingenuous.
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"We launched strikes against Sinjar, and the other place (in Syria) and killed 210 to 220 terrorists there. Why?"
The Britain-based Syrian Observatory for Human Rights, a monitoring group, said the Syrian Democratic Forces' control of Tabqa was "practically total".
This is not the first time that Turkey has attacked us.
"We can come unexpectedly in the night", Erdogan said.
Tension between Turkey and the YPG has been rising. Turkey fired a barrage of artillery at the YPG, who returned fire with rockets on Turkish outposts on the border.
This means American forces have been forced to intervene between two of their own allies, with Turkey being a member of North Atlantic Treaty Organisation.
Turkey has made clear it will use force to prevent the development of a Kurdish-controlled area on its Syrian doorstep.
"We are telling American friends so as not to take a terror group along with them", the Turkish leader said. "From the Canton of Efrin to Cindirês, and further to Dirbesiyê of the Cezire Canton, many points of our forces were attacked by the Turkish army", the YPG said.
ISIK's Aamaq news agency claimed ISIL fighters killed 30 government soldiers in the attack on Um Mayyal. Local residents attested that intermediaries from Raqqa and Aleppo arrived to pick up the oil and often mentioned Turkey, while a captured ISIS recruit admitted on camera that the terrorist group sells oil to Turkey.