The tragic milestone means that about one of every eight Syrians is now fleeing across the border, and 6.5 million others have been displaced with the country's borders, the Geneva-based agency, which also noted that over half of all those uprooted are children.
"The Syria crisis has become the biggest humanitarian emergency of our era, yet the world is failing to meet the needs of refugees and the countries hosting them," said UN High Commissioner for Refugees Antonio Guterres.
The massive numbers of Syrians fleeing the civil war also has stretched the resources of neighboring countries and raised fears of violence spreading in the region.
The UN estimates there are nearly 35,000 more awaiting registration as refugees, and hundreds of thousands who are not registered.
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The refugee agency and other aid groups say an increasing number of families are arriving in other countries in shockingly poor condition, exhausted and scared and with almost no financial savings left after having been on the run for a year or more.
Lebanon hosts 1.14 million Syrian refugees, the single highest concentration of them, but Turkey has 815,000 and Jordan has 608,000.
The agency says regional governments estimate hundreds of thousands more Syrians are seeking sanctuary in their borders without registering as refugees.