Russia said it planned to push for dialogue between the Syrian and Turkish governments following the incursion.
Turkey has "legitimate concerns about the safety of its borders" but had not been able to properly raise them with Damascus as this was "made difficult by the actions of the Americans and the coalition" east of the Euphrates river, Foreign Minister Sergey Lavrov said.
"We have warned for many years about the extreme danger of the experiment that the Americans were staging there in an effort to pit the Kurds against Arab tribes," Lavrov told journalists in Turkmenistan.
"We warned against playing the Kurdish card because it can end badly."
Italy condemned the Turkish offensive as "unacceptable", saying military action in the past always led to "terrorism".
The French foreign ministry, meanwhile, called in Turkey's ambassador for a meeting later on Thursday.
"He will be summoned this afternoon following the offensive on Syria," said a diplomatic source, speaking on condition of anonymity.[mr/aje]