Melkite Greek Catholic Patriarch Gregorios III said the "almost communal wave of youth emigration" is now so severe it begged serious questions about the future of the Church in Syria.
In an open letter to the youth, the Damascus-based prelate said emigration of Christian young people was especially severe in Syria but was also of grave concern elsewhere in the Middle East.
He stated: "The almost communal wave of youth emigration, especially in Syria, but also in Lebanon and Iraq breaks my heart, wounding me deeply and dealing me a deadly blow.
"Given this tsunami of emigration... what future is left for the Church? What will become of our homeland? What will become of our parishes and institutions?"
Recognising the many problems of life in Syria today, the Patriarch said he wanted to "implore" young people to remain.
He stated: "Despite all your suffering, stay! Be patient! Don't emigrate! Stay for the Church, your homeland, for Syria and its future! Stay! Do stay!"
Meanwhile, Germany has criticised David Cameron over Britain's failure to take its fair share of migrants fleeing Syria and Afghanistan.
A spokesman for Angela Merkel's party has told The Times the prime minister could be jeopardising his hopes to renegotiate the UK's relationship with the EU.
Hundreds of refugees have been stranded in Budapest overnight, after police stopped them from getting on trains to Germany and Austria.
Mark Stone, Skys correspondent in Budapest told Premier's News Hour that people often ask: "How many of them as so called 'economic-migrants' just looking for a better life elsewhere and how many of them are genuinely fleeing war in their own country? And from those we've spoken to over the last 24 hours or so, they are all the latter - they are fleeing cities like Apelo in Syria which have been utterly destroyed by the war there."
He stressed that there are opposing opinions in the city about what to do regarding the influx of refugees: there's "split opinion - I mean clearly we haven't done any sort of survey, but we have spoken to some last night.
"A family of Hungarians, clearly very well off, turned up in a brand new BMW four wheel drive, opened up the back and it was full of food - and they got the food out and they handed it out to some of the people sitting out here.
"They were very, very struck and very upset by what was unfolding on their own streets.
"But then this morning I spoke to a man who was telling me that all these people should go home - he was talking about terrorism, he was saying that this was a modern day invasion - a very, very different and very hard line view.
"So split opinions and I think you're seeing both extremes in terms of the people that are here - and those extremes are demonstrated here as well in terms of the politics of Europe."
Anti-persecution charity, Aid to the Church in Need says because of the state of flux in Syria, no precise figures are available concerning the country's Christian population.
But, according to conservative estimates, 450,000 of Syria's pre-2011 Christian population of 1.17 million are either internally displaced or living as refugees abroad.
The Christian population has suffered especially badly as cities with a high concentration of faithful - including Aleppo and Homs - have seen some of the worst fighting and upheaval.
Middle East analysts have warned of Syria experiencing a repeat of the crisis in Iraq where Christian numbers have haemorrhaged from 1 million to less than 300,000 over the past 10 to 15 years.
Encouraging Syria's Christian youth to persevere in their homeland, Patriarch Gregorios pointed to episodes from the past where the Church quickly recovered after outbreaks of persecution.
He highlighted a revolution in Syria in 1860 involving the killing of thousands of Christians and the destruction of many churches in Damascus Old City before adding: "Our forebears underwent great difficulties, but they exercised patience and so the Church remained, Christianity remained and the number of Christians even grew after 1860."
Listen to Premier's Des Busteed speak to Mark Stone here: