Church leaders in north-eastern Syria have expressed fears that some members of the Turkish and Syrian forces will "pursue an Islamist agenda".
Cities in the region have come under "enormous air and military bombardment" since the Turkish military offensive began last week, they report.
Up to 50,000 Christians in the region stand to be affected, Open Doors UK warns.
Pastor George, a Christian leader from the Alliance Church in Qamishli, close to the Turkish border, told Open Doors that he fled with his family and church members on Saturday.
"There was a lot of shelling yesterday on the border. Some homes were completely destroyed," he said.
Another church leader told Open Doors that there has been "shelling and severe armed clashes" near the border town of Kobani.
The north-eastern region of Syria is home to many Christians and some church leaders have told the organisation of their fears that some within the Turkish forces and their Syrian opposition allies are pursuing Islamist agendas hostile to Kurds and those who are not Sunni Muslim.
Some of the Christians in the region are converts from Islam and the church leaders have warned that they are particularly vulnerable.
In some parts of Syria, Islamic extremists continue to hold control and are forcing Christians to follow strict dress codes and pay protection money. In these areas, the Christians have not been able to follow their faith in public.
The leaders of historical churches have also become targets for abduction and in some cases, Christians have been kidnapped for ransom.
Open Doors said there was no evidence at the moment that Christians are being deliberately targeted in the latest conflict.
But the organisation warned that "the threat of extremist action will be compounded if the security of prisons holding suspected Islamic State militants is compromised during the intense fighting".
Open Doors has helped over 30,000 Christian families in Iraq and Syria since 2016, providing relief, microloans, work training, and rehabilitation projects.
It fears that this newest wave of conflict will set back the progress that has been made in rehousing many of them and helping them to rebuild their communities and livelihoods.
"Open Doors' partners have worked hard to settle Christians back into their homes after their displacement from earlier conflicts and this new offensive will put their lives in danger and may force them to flee once again," said Henrietta Blyth, CEO of Open Doors UK and Ireland.
In the face of yet more upheaval and many families facing the difficult decision of whether to leave, the charity is working with church partners in the region to help them prepare for the possibility of thousands of Christians fleeing the border areas.
"We will keep a very close eye on the needs of the local church but, for now, we will continue our projects in the area distributing food and medical aid and rolling out winter survival packs," said Mrs Blyth.
"We hope and pray that the political and military leaders involved in this latest conflict will act with restraint and compassion as, once again, tens of thousands of people in Syria are facing displacement from their homelands."