The United States-led coalition has carried out a series of air strikes on Islamic State militants this week in Iraq and Syria after the terror outfit reportedly kidnapped around 250 Assyrian Christians.

The US and its partner nations launched 14 air strikes, the Combined Joint Task Force said.

According to the Syrian Observatory for Human Rights the raids struck areas around the town of Tal Tamr in Hasakeh province in northeastern Syria near Kobani.

In Iraq tactical units of the Islamists were targeted near Al Asad, Fallujah, Mosul and other locations, a statement said.

Tal Tamr remains under the control of Kurdish forces, but at least 10 surrounding villages have been seized by IS militants, along with the captives, many of whom are said to be women, children and elderly.

Negotiations for the release of the captives are ongoing the Syrian Observatory for Human Rights said "through mediators from Arab tribes and a member of the Assyrian community".

As many as 35 jihadists and 25 members of the Kurdish People's Protection Units (YPG) have been killed in a fierce fighting that started after Assyrian Christians were abducted by IS militants, the Observatory said.

More than 5,000 people have fled from the countryside, most of them seeking refuge in Qamishli, a city that is controlled by Kurdish forces.

AFP quoted Jean Tolo, of Qamishli's Assyrian Organisation for Relief and Development as saying: "We've received around 200 families who are being hosted in local homes."

"The people arriving are desperate. They are coming with nothing, they left everything behind."

The US State Department has condemned the kidnappings and said: "ISIL's [another name for the terror group] latest targeting of a religious minority is only further testament to its brutal and inhumane treatment of all those who disagree with its divisive goals and toxic beliefs."