The abductions appeared to be in retaliation for a major Kurdish offensive aimed at recapturing nearby villages, and which has killed 132 jihadists in four days, said the Syrian Observatory for Human Rights.
The Britain-based monitor said IS kidnapped the Assyrians today after seizing two villages, Tal Shamiram and Tal Hermuz, in Hassakeh province from the control of the Kurdish People's Protection Units (YPG).
The group had no immediate details on those kidnapped, including whether women and children were among them, or where they were being held.
"The fighting around Tal Hamis has killed at least 132 jihadists in four days, and four YPG fighters today alone," he added.
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"A fifth man, a Westerner who had travelled into Syria to fight alongside the YPG, was also killed."
There were just 30,000 Assyrians in Syria before the country's conflict erupted in March 2011, with most of them living throughout Hassakeh province.