Fr Pierbattista Pizzaballa was speaking before an international conference focusing on the exodus from Syria is held in London.
At the conference, the United Nations called for another £5.29bn to help Syria's humanitarian crisis.
According to the Catholic anti-persecution charity Aid to Church in Need (ACN), the British government has pledged £1.17m so far.
This does not include the promise to take in 20,000 Syrian refugees by 2020.
The government has also agreed to take in an yet unspecified number of vulnerable children from refugee camps around Syria, and pledged £10m towards vulnerable refugee children who've already travelled to Europe.
Father Pierbattista Pizzaballa told ACN: "Under no circumstances would I encourage the Christians to emigrate.
"We are doing everything in our power to make it possible for the Christians to stay.
"I would tell them: Go to a safe part of the country, but stay in Syria...
"I would tell the politicians in Europe, it would be better to help the refugees, including the Christians, here than in Europe.
"It would be better to invest the money required to assist the millions of refugees here. It is better for both the refugees and the region."
