"We will make any kind of contribution to the work to clear Daesh (IS) from Syria," Erdogan told a rally in the southern city of Gaziantep, near the Syrian border.
"For the issue of the PYD (Democratic Union Party) terror group in Syria, we have just the same determination," he added, referring to the main pro-Kurdish party in northern Syria and its People's Protection Units (YPG) militia.
Ankara said its raids had killed 25 Kurdish "terrorists" and that the army was doing everything it could to avoid civilian casualties.
But the Britain-based Syrian Observatory for Human Rights said at least 40 civilians were killed in strikes on two areas - the first report of significant civilian casualties since the start of operation "Euphrates Shield."
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The monitor also said at least four Kurdish fighters had been killed and 15 injured in the bombardments south of Jarabulus, the town taken from IS by Turkish-backed Arab rebels on the first day of Turkey's incursion Wednesday.
"We will absolutely not allow any terror activity on or near our borders."
Gaziantep is the city where a suicide bomber blew himself up in the middle of a wedding party last weekend, killing 55 people.
Turkey blamed the attack on the Islamic State group. Erdogan reaffirmed a previous statement that the bomber was a child aged just 14.
Days later Ankara launched the two-pronged Syria operation with the stated aim of clearing the border area of both IS and the Kurdish fighters.
The US supports the Syrian Kurdish fighters as an effective adversary of IS in the area.