The Syrian Kurdish Peoples' Protection Units (YPG) are seen by Washington as the most effective fighting force in the battle against jihadists in Syria.
Ankara says the fighters of the YPG are merely the Syrian branch of the Kurdistan Workers' Party (PKK), who have waged an insurgency since 1984 inside Turkey that has left tens of thousands dead.
Turkish forces last week carried out air strikes on YPG positions in Syria, angering the United States and sparking days of border clashes with the Kurdish fighters.
The US sent military vehicles with American flags to the Syrian side of the frontier accompanied by YPG fighters to carry out patrols, in an apparent bid to prevent further fighting.
"Unfortunately... the presence of an American flag along with the (insignia) of a terror organisation called YPG in a convoy has seriously saddened us," Erdogan told reporters in Istanbul before heading on a trip to India.
The difference of opinion over the YPG has cast a shadow over US-Turkish relations for some time and Erdogan is hoping for a drastic change in US policy when he meets President Donald Trump next month.
"We will bring this up when we meet Mr President on May 16," said Erdogan.
He expressed regret that the US-YPG cooperation -- which began under the former Barack Obama administration -- was being continued under the new president.
"This needs to be stopped right now," said Erdogan. "Otherwise it will continue to be a bother in the region and for us."
"It will also bother us as two NATO countries and strategic partners," he said.
Erdogan reaffirmed that Turkey could again bomb the YPG positions at any time it wanted.
"I said yesterday: 'We can come unexpectedly in the night'. I really meant that. We are not going to tip off the terror groups and the Turkish Armed Forces could come at any moment."
"Better they live in fear than we have worries," he said.
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