Deadly clashes were erupted between the Kurdish fighters and members of the al-Qaeda-lined Islamic State of Iraq and the Levant on Wednesday and extended to Thursday.
Some 13 Kurds also died in the fighting, reports say.
The foreign-backed militants and other terrorists have sought to take over Kurdish towns in the region, particularly those along the Turkish border or those near key oil facilities, and the attacks have sparked an exodus of Kurdish civilians into neighboring Iraq, along with a threatened intervention by Iraqi Kurdistan.
The fighting has also led to increased militarization among Kurdish militias, which before the war had relatively limited influence in the Syrian region, and has now mobilized large amounts of the population to resist the al-Qaeda takeover.
The United Nations High Commissioner for Refugees (UNHCR) says more than 40,000 Syrians fled their country to seek refuge in Iraq's Kurdistan region in recent days amid escalating violence by foreign-backed militants.
Most of the refugees are Syrian Kurds, who fled Syria following attacks by foreign-backed Takfiri militants in the country.
The influx of the Syrian Kurd refugees to Iraq's Kurdistan region comes after al-Qaeda-linked al-Nusra Front started attacks on several Kurdish-majority areas in northern and northeastern Syria, killing a large number of civilians, including many women and children.
Syria has been gripped by deadly unrest since 2011.
A very large number of the militants operating inside Syria are reportedly foreign nationals.
According to reports, the West and its regional allies - especially Qatar, Saudi Arabia, and Turkey - are supporting the militants inside Syria.