A Syrian Christian group representing several NGOs inside and outside the country said it had verified at least 150 people missing, including women and the elderly, who had been kidnapped by the militants.
"We have verified at least 150 people who have been abducted from sources on the ground," Bassam Ishak, president of the Syriac National Council of Syria, whose family itself is from Hasaka, told Reuters from Amman.
Earlier the British-based Syrian Observatory for Human Rights said 90 were abducted when the militants carried out dawn raids on rural villages inhabited by the ancient Christian minority west of Hasaka, a city mainly held by the Kurds.
Hundreds of others remain trapped in villages surrounded by ISIS fighters in violence that has displaced more than 3,000 people.
Syrian Kurdish militia launched two offensives against the militants in northeast Syria on Sunday, helped by U.S.-led air strikes and Iraqi peshmerga.
This part of Syria borders territory controlled by ISIS in Iraq, where it committed atrocities last year against the Yazidi religious minority.
ISIS did not confirm the kidnappings. Supporters posted photos online of the group's fighters in camouflage attire looking at maps and firing machine guns. The website said the photos were from Tel Tamr, a town near where the Observatory said the abductions occurred.
Many Assyrian Christians have emigrated in the nearly four-year-long conflict in which more than 200,000 have people have been killed. Before the arrival of Kurds and Arab nomadic tribes at the end of the 19th century, Christians formed the majority in Syria's Jazeera area, which includes Hasaka.
Sunday's offensive by Kurdish YPG militia reached within five km (3 miles) of Tel Hamis, an ISIS-controlled town southeast of Qamishli, the Observatory said.
At least 14 ISIS fighters died in the offensive, in which Assyrians fought alongside Kurds, it added. Kurds by heavy shelling could seized several Arab villages from ISIS control.
Last year, ISIS fighters abducted several Assyrians in retaliation for some of them fighting alongside the YPG. Most were released after long negotiations.