|Photo posted by al-Baraka division of Islamic State purportedly shows militants|
battling Kurdish and Christian militia near Tal Hamr, Hassakeh province, Syria
Initial reports had put the number of missing at 90, but one activist said as many as 285 people had been seized on Monday in Hassakeh province.
Efforts to try to negotiate their release are reported to be under way.
Some 1,000 local Assyrian families are believed to have fled their homes in the wake of the abductions.
Kurdish and Christian militia are battling IS in the area, amid reports of churches and homes having been set ablaze.
Thousands of Christians in Syria have been forced from their homes by the threat from IS militants.
In areas under their control, Christians have been ordered to convert to Islam, pay jizya (a religious levy), or face death. IS militants in Libya also recently beheaded 21 Egyptian Coptic Christians.
The Assyrians were seized by the militants as they swept into 12 villages along the southern bank of the Khabur river near the town of Tal Tamr before dawn on Monday.
The Syrian Observatory for Human Rights, a UK-based activist group, said at least 90 people had been abducted, most of them women, children and the elderly.
However, the Syriac National Council of Syria put the figure as high as 150, while Afram Yakoub of the Assyrian Federation of Sweden said sources on the ground had told him that up to 285 people were missing, including 156 from the village of Tal Shamran and 90 from Tal al-Jazira.
"These were peaceful villages that had nothing to do with the battles," Nasir Haj Mahmoud, a Kurdish official in the YPG militia in north-eastern Syria, told the Reuters news agency.
There are conflicting reports as to where the families have been taken.
Kino Gabriel, a spokesman for the Syriac Military Council - a Christian militia fighting alongside the Kurdish Popular Protection Units (YPG) - told the BBC that it believed the captives had been taken to Abdul Aziz mountain.
Osama Edward of the Sweden-based Assyrian Human Rights Network told the AFP news agency that the captives had been taken to the IS stronghold of Shaddadi, as did Syria's state news agency, Sana.
Another report said they were in Raqqa, 145km (90 miles) to the west, the de facto capital of the "caliphate" declared by IS last June.
The BBC's Jonny Dymond in Beirut says the motive for the seizure of so many Assyrians is not yet clear. Our correspondent says it may be that the captives are to be used as part of a swap with the Kurdish forces.
Hundreds of Assyrians who were living in villages on the north bank of the Khabur river and elsewhere are reported to have fled following the attack to the largely Kurdish-controlled provincial capital of Hassakeh, to the south-east, and Qamishli, another city to the north-east.
|Photograph posted by Syrian Kurdish Popular Protection Units (YPG)|
shows militiamen near Tal Tamr (24 February 2015)
Kurdish and Christian fighters are battling IS militants in the area
where the Assyrians were abducted
Mr Gabriel said IS had moved a big force into the area and were trying to take control of Tal Tamr.
The Syriac Military Council had about 400 fighters in the area and at least four had been killed in clashes with the jihadists, he added. The YPG has deployed between 1,000 and 1,500 fighters.
The YPG is also continuing a major offensive launched on Sunday against IS some 100km (60 miles) to the east, near the border with Iraq - an area of vital importance to the jihadists.
Please pray for these Christians, in particular the women and girls. We do not know that they will be used as bargaining chips, or if they are, what will happen if the negotiations fail. It is also quite possible the prisoners will be used as human shields against air strikes. The women and girls could also be in danger of being used as sex slaves, or sold to fighters for wives. All prisoners are in danger of forced conversion or possible beheading. Please pray.