Turkey, which backs Syrian rebel groups and which launched a ground operation in northern Syria past year, has vowed to continue acting against groups it links to the outlawed Kurdistan Workers' Party [PKK].
The airstrikes were Turkey's first in Syria since it announced the end of a ground operation against Kurdish militants and Islamic State there in March, without withdrawing its troops.
U.S. officials said they were "deeply concerned" after Turkey carried out a series of airstrikes Tuesday against USA allies fighting ISIS in Syria and Iraq.
Moreover, the strikes early on Tuesday morning also killed at least five fighters of the peshmerga, the armed forces of the Kurdish autonomous region in Iraq who are another US partner in the fight against ISIS.
Toner said any military action in Iraq should be approved by that government.
"We encourage all forces to. concentrate their efforts on ISIS and not toward objectives that may cause the Coalition to divert energy and resources away from the defeat of ISIS in Iraq and Syria", it said, using an acronym for the Islamic State.
Turkish President Tayyip Erdogan has said he will not allow Sinjar, around 115 km (70 miles) from the Turkish border, to become a "new Qandil", referring to a PKK stronghold in Iraq near the borders with Turkey and Iran. This could greatly complicate United States support for both sides, and the Kurds having to shift toward resisting Turkish incursions would likely derail their planned invasion of the ISIS capital of Raqqa.
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Turkish warplanes on Tuesday struck targets on Sinjar Mountain in northern Iraq as well as a mountainous region in Syria. The U.S. has backed the YPG with advice and training as part of the Syrian Democratic Forces and "we will continue that support".
Lavrov told a security conference on Wednesday the attack as a pretext for a regime change in Syria and said the USA response "pushes the prospect for a wide worldwide front on terror even further away". "We respect Syria and Iraq's territorial integrity", but Turkey had "a legitimate right with these interventions" because of the threats to Turkey posed by the YPG and the PKK.
A separate series of strikes hit a base near Sinjar in northern Iraq, close to the Syrian border.
Mortar shells fired from an area in Syria controlled by the Kurdish Peoples' Protection Units (YPG) hit an army command post in the Akcakale district of Turkey's southern Sanliurfa province, the Dogan and Anadolu news agencies said. Kurdish sources said that 20 fighters died in the attack.
The air strikes in Syria targeted the YPG, a key component of the Syrian Democratic Forces (SDF), which are backed by the United States and have been closing in on the Islamic State bastion of Raqqa.
Foreign Minister Mevlut Cavusoglu said: "Two hours before this operation, we shared information with the United States and Russian Federation that we would undertake an operation" in the region. Abdel Rahman said a female Kurdish fighter was among the dead.
Due to its ties with the PKK, Turkey regards it a terrorist organisation that threatens its internal security. The Syrian Kurds have driven IS from large parts of Syria and are now closing in on Raqqa, the de facto capital of the extremists' self-styled caliphate.