IS fighters kidnapped at least a hundred Christians as they entered Hassakeh province on Monday. It's thought many of those taken by the militants were women, children and the elderly.
Reports suggest at least 12 mainly Christian villages have been captured by the Muslim jihadis.
Images show entire families taking what belongings they can in plastic bags and boarding trucks and buses to leave the region.
Archbishop at the Syrian Orthodox Church Athanasios Dawood told Premier they were told to convert to Islam or be killed.
The same ultimatum was given by IS to Christians living in the Iraqi city of Mosul last year.
Assyrian christian villages in khabur #syria which were attacked by isis #Assyrian #ISIS #Tell_Tamer #Hasakah pic.twitter.com/bcaSVBozqU
— steven nabil (@stevoiraq) February 24, 2015Kurdish fighters are battling IS in Hassakeh but reporters on the ground say they're outnumbers by militants.
Archbishop Dawood said it was a 'disaster situation'.
"We need support, we need help. Where is the United Kingdom, where is the United Nations, where is America?" He asked.
"Why do they allow IS to kill people and occupy our villages, why?"
He added: "No one cares about the Christians. This is what is hurting our hearts, they should support us, nobody is supporting us."
He told Premier it was becoming clear that Islamic State would force every Christian in the areas it controls to convert to Islam or die.
The Church leader said there was a need for supplies to help the families who have ended up refugees.
"They need some help. Food, water, medicine as some people are injured.
"They need material for sleeping like blanket and heaters.
"It's really a disaster situation now."
US State Department spokeswoman Jen Psaki said: "IS'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.
"To bring an end to these daily horrors, we remain committed to leading the international coalition to degrade and defeat IS."
Yesterday the coalition led by the US reported that it had carried out three airstrikes on IS targets in Hassakeh province.
The United Kingdom is taking part in strikes in Iraq but not Syria.
Assyrian Christians are one of the world's oldest Christian communities and have been in the Middle East for thousands of years.
Listen to Premier's Antony Bushfield's interview with Archbishop at the Syrian Orthodox Church Athanasios Dawood: