The charity says labelling the believers in the region this way is both unhelpful and degrading.
Explaining why, Tim Livesey, Embrace the Middle East's CEO told Premier: "It's very demoralising and it's the opposite in a sense I think of what Christians in the Middle East would like us to be thinking.
"They would like us to think that they are in many ways really very special and within the Christian global context, very important - and they are."
Christians make up approximately 5 per cent of the population in the Middle East - down from 20 per cent in the early 20th century.
However, Livesey said the decline can't solely be put down to the desire by extreme elements within the Muslim majority to eradicate Christianity from the region.
"Persecution is pretty rare... when ISIS was [more active] in Iraq for example - for sure there was persecution of Christians but also of course of non-Christians," he said.
"So it's not to say that there isn't violence in the region - there is - and Christians, along with people of other faith, suffer from that."
The charity and its partners held an event in Westminster on Thursday to discuss with Parliamentarians and policy makers what life is really like for Christians in the region.
Dr Souraya Bechealany, acting general secretary of the Middle East Council of Churches said Westerners need to come and see for themselves how Christians in the Middle East are living.
She explained: "The reality on the ground in the Middle East is complex and plural. It cannot be reduced to one simple narrative or another.
"The best way to better comprehend our reality is to come and see. Then you can speak to what you have actually seen, heard and experienced."
Livesey told Premier it was time for Christians in the West to have a greater appreciation of the contribution of Christians to Middle Eastern society.
He added that Christians in the West could learn a lot from the people they wrongly label.
"I regard working with Christian partners in the Middle East the most incredible privilege and very humbling and I genuinely mean that. It can only help my faith and it can only help me better understand the gospel.
"I would encourage people - and I know that Christians in the Middle East would encourage people - if you ever get the opportunity to travel to the region, not to stay in a hotel or to swim at the beach... but to meet Christians, you will never look back. I promise you."
Listen to Tim Livesey speaking with Premier's Eno Adeogun:
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.
