The raids struck areas around the town of Tal Tamr in Hasakeh province, the Syrian Observatory for Human Rights said, without giving information on possible casualties.
They followed the launch Monday of a new offensive by IS, which kidnapped the Assyrians as it seized territory around Tal Tamr.
The town remains under the control of Kurdish forces, but at least 10 surrounding villages have been seized by IS, along with the captives.
Many of those abducted are said to be women, children or elderly.
The Observatory said negotiations were ongoing “through mediators from Arab tribes and a member of the Assyrian community” to secure their release.
The IS offensive has killed at least 35 militants and 25 members of the Kurdish People’s Protection Units (YPG) and of an Assyrian defence force, according to the Observatory.
Thousands flee IS advance
The fighting and kidnappings prompted around 5,000 people to flee the countryside, with many seeking refuge in Qamishli, a large city in the province that is controlled by Kurdish and regime forces.
“We’ve received around 200 families who are being hosted in local homes,” Jean Tolo, of Qamishli’s Assyrian Organisation for Relief and Development, told AFP.
“The people arriving are desperate. They are coming with nothing, they left everything behind.”
Others made their way to Hasakeh city, the provincial capital, describing harrowing journeys after fleeing in their pajamas.
The United States and United Nations denounced the mass abduction of Christians — the first of its kind in the country — and demanded their release.
“ISIL’s 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,” State Department spokeswoman Jen Psaki said, using another acronym for IS.
Osama Edward, director of the Assyrian Human Rights Network, told AFP Wednesday he believed the abductions were linked to the militants’ recent loss of ground in the face of US-led air raids.
“They took the hostages to use them as human shields,” he said.
The jihadists, who are battling Kurdish fighters on the ground, may try to exchange the Assyrians for IS prisoners, he said.
Before Syria’s civil war erupted in 2011, there were 30,000 Assyrians in the country, among an estimated Christian population of about 1.2 million.
‘Jihadi John’ identified
IS is accused of multiple abuses against minorities in the areas under its control in Iraq, Syria and elsewhere.
Last week, a video emerged showing its fighters in Libya beheading 21 Christians, most of them Egyptian Copts.
Such grisly videos have become a hallmark of the group, with one British-accented militant from the organisation appearing in multiple videos showing killings of foreign hostages.
On Thursday, experts and media identified the man dubbed “Jihadi John” by the British tabloids as Kuwaiti-born London computer programmer Mohammed Emwazi.
He was first named by the BBC and Washington Post, with the International Centre for the Study of Radicalisation think tank saying it believed the identity to be “accurate and correct”.
More than 210,000 people have been killed since Syria’s war began in March 2011.
The conflict began with peaceful pro-democracy protests against President Bashar al-Assad but escalated into a civil war that brought foreign jihadists flocking to the country.
In other developments, UN peace envoy Staffan de Mistura will travel to Syria for talks about a new plan for a six-week freeze of fighting in Aleppo, the UN spokesman said.
“He will be heading to Damascus on Saturday to meet with senior Syrian government officials to follow up, obviously, on the cessation of hostilities and to have further consultations,” Stephane Dujarric said.
De Mistura said earlier this month that Damascus was willing to suspend aerial bombardment and artillery fire on Aleppo for six weeks.
A group of French lawmakers met Assad on an unofficial trip on Wednesday, drawing criticism from French President Francois Hollande.
“I condemn it because French lawmakers have taken it upon themselves to meet with a dictator who is the cause of one of the worst civil wars of recent years,” Hollande said. —