In Washington, the State Department said it was deeply concerned by the air strikes, which were not authorized by the USA -led coalition fighting Islamic State in Iraq and Syria.
Deputy spokesman Mark Toner said the Middle East is a "complex battle space", but he warned "Turkey can not pursue that fight now at the expense of our common fight against the terrorists that threaten us all and that obviously means ISIS".
Toner stressed the United States will continue to press the case with Turkey that all of the forces fighting Daesh (outlawed in Russia) in that region need to focus on the goal to combat the terror group.
The YPG - which is part of the Washington-backed Syrian Democratic Forces (SDF) - have called on the U.S. to implement a no-fly-zone in northern Syria, to prevent further Turkish airstrikes.
Turkey is part of the US -led military coalition fighting militants in Syria.
The PKK is listed as a terrorist organization by Turkey, the USA and European Union and Turkey also considers its Syrian affiliate the PKK/PYD a terror group. The coalition had forces within six miles of the strikes, he added, but none were put in harm's way by the strikes.
Then on Tuesday, the Turkish Air Force conducted air strikes near Sinjar, Iraq "without proper coordination with the coalition or the government of Iraq", Dorrian said.
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Foreign Minister Mevlut Cavusoglu said on Wednesday that the Turkish military had informed Washington and Moscow on the attack a day earlier that targeted Kurdish-dominated areas in Syria and neighboring Iraq. USA officials said that they had asked Turkey not to proceed without proper coordination but that the request was ignored.
The Turkish warplanes on Tuesday conducted airstrikes targeting the positions of the Kurdistan Workers' Party (PKK) in northern Iraq, killing at least five Iraqi Kurdish fighters and wounding ten others, Xinhua news agency cited local Kurdish media reports.
Fighting is growing along the border between Turkey and Syria today, as following yesterday's major Turkish airstrikes against Kurdish targets, the two sides are now trading artillery fire back and forth in the area.
North Atlantic Treaty Organisation member Turkey considers the YPG an extension of the Kurdistan Workers' Party, or PKK, which has been waging an insurgency in Turkey since 1984.
"We recognize the threat the PKK poses to Turkey, but Turkey can not pursue that fight at the expense of our common fight against terrorists that threaten us all", Rankine-Galloway said, using the initials for the Kurdistan Workers' Party.
In a statement, the Turkish military said "the determined terrorist targets were hit" and that it had struck because of weapons being carried into Turkey.