Turkey said it had carried out the strikes in northeastern Syria and northern Iraq against "terrorist havens" and vowed to continue action against groups it links to the outlawed Kurdistan's Workers' Party (PKK).
In northeastern Syria strikes targeting the Kurdish People's Protection Units (YPG) -- who are leading the offensive against IS stronghold Raqa -- killed at least 18 people.
In northern Iraq they killed six peshmerga fighters from the autonomous Kurdish government, usually allied with Ankara, in an apparent accident. The peshmerga said the strike was "unacceptable" but blamed PKK-affiliated militia who were the apparent targets.
They could also exacerbate tensions between Ankara and its NATO ally Washington, which sees the Kurds as one of the most effective fighting forces against IS.
Turkey's army said it launched the strikes "in order to destroy terrorist havens targeting our country".
"The operations will continue to be carried out from now with the same determination until the very last terrorist is neutralised," the army said.
The bombardment in northeastern Syria saw Turkish planes carry out "dozens of simultaneous air strikes" on YPG positions overnight, including a media centre, a monitoring group said.
In a statement distributed to journalists, the YPG confirmed the Turkish bombardment and said there were casualties but did not give a toll.
Representatives of the US-led coalition visited the site of the air strikes on Tuesday, the YPG's political arm, the Democratic Union Party (PYD), said on Twitter.
The PYD published photographs of YPG officials walking alongside a man in a military uniform with a patch bearing a US flag on his chest.
"It's unthinkable that we are fighting on a front as important as Raqa while Turkish planes bomb us in the back," the commander said.
Ankara has bombed the YPG across swathes of northern Syria for months, calling it a "terrorist" group because of its ties to the PKK, which has been waging a deadly insurgency against the Turkish state since 1984.
While the air raids on Syria appeared to hit their intended targets, the bombardment in Iraq instead killed members of Kurdish security forces that are typically allied with Ankara.
Turkey appeared to have been targeting a minority Yazidi militia allied with the PKK and based in the northwestern region of Sinjar.
The peshmerga denounced the strike as "unacceptable" but focused blame on PKK-affiliated groups.
"These problems and tensions are all because of the PKK's presence," it said.
The peshmerga have been instrumental in the battle against IS in northern Iraq though have stepped back in recent weeks as Iraqi forces advance against IS in Mosul.
Iraqi forces today announced they had retaken full control of the Tenek district, one of the largest neighbourhoods in west Mosul.
IS is facing multiple offensives across Syria and Iraq -- often led by governments or forces that are otherwise bitterly opposed to each other.
Turkey launched an unprecedented cross-border operation into Syria in August to fight IS and to keep the YPG in check.
The YPG makes up the bulk of the Syrian Democratic Forces (SDF), an alliance of Kurdish and Arab fighters taking on IS jihadists in Syria.
After chipping away at IS territory across the country's north, the SDF is now locked in clashes against the jihadists inside Tabqa, a key town on the Euphrates River.
The SDF entered the town on Monday as part of their flagship offensive for Raqa, the Syrian heart of the jihadists' self-styled "caliphate" since 2014.
More than 320,000 people have been killed in Syria's six-year conflict, which the World Health Organization has called the most dangerous place for health workers.
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