Turkey views some of the Syrian Kurdish forces assisting the US -led coalition's campaign against ISIS as terrorists, and in a statement Wednesday, the spokesman for Turkey's foreign ministry, Huseyin Muftuoglu, defended the strikes.
The airstrikes also killed five members of the Iraqi Kurdish militia known as the peshmerga, which is also battling the extremist group with help from the US -led coalition.
Toner said any military action in Iraq should be approved by that government.
Toner said coordination is essential "to maintain pressure to destroy ISIS on the battlefield" and also to "ensure the safety of all coalition personnel" operating in the region.
President Recep Tayyip Erdogan had earlier singled out Mount Sinjar as a possible target, saying "terrorists" were trying to turn the area into a launchpad for attacks against Turkey.
That included, the ministry said, notifying the USA air command center in Qatar and speaking with the head of the US military.
The United States on Tuesday expressed "deep concern" over the air strikes.
A military statement said the air strikes targeted the Zap region, the Turkish name for a river which flows across the Turkish-Iraqi border and is known as Zab in Iraq.
"Less than an hour of notification is an inadequate amount of time to have our forces leave the ops box area that was identified ... which was a very large ops box", he said, referring to the area in which USA forces are operating.
Turkey has signaled its intention to pursue its own aims in Syria regardless of the desires of Europe or the US.
Turkey's defense minister said the PKK would not be allowed to establish a presence in northern Iraq.
There were no casualties but minor material damage.YPG spokesman Redur Xelil said there was heavy Turkish artillery fire across the border into Syria on Wednesday.
Turkey attacked two Kurdish positions on Tuesday, hitting a local YPG military headquarters in north-east Syria and a Peshmerga position in Iraq's Sinjar Mountains.
Marine Maj. Adrian Rankine-Galloway, a Pentagon spokesman, said Turkey must prioritize the fight against IS.
Iraqi Kurdish authorities also demanded the withdrawal of Kurdistan Workers Party (PKK) fighters from northern Iraq's Sinjar region after the attacks.
Russian Federation on Wednesday criticized Turkey's airstrikes against Kurdish forces in Syria and Iraq, saying they hindered efforts to combat the Islamic State group, as Turkish troops and Syrian Kurdish fighters traded fire across the increasingly tense frontier.
The targets were hit to prevent PKK from sending "terrorists, arms, ammunition and explosives to Turkey", the statement said, adding that the operation was conducted "within the scope of the global law".
Turkey has regularly bombed the mountainous border area between Iraq and Turkey where PKK militants are based since a ceasefire broke down in July 2015.
The SDF and the Syrian government have largely avoided confrontation over the course of the complex civil war.
In April past year, the USA ambassador to Ankara denied arming the PKK/PYD and said any US weapons found in PKK hands would have ultimately come from Iraqi security forces. In a statement, the YPG said 20 of its fighters were killed.