BEIRUT, Lebanon — The number of registered Syrian war refugees who have flooded into Lebanon exceeded one million on Thursday, the United Nations said, describing it as a devastating milestone in a humanitarian crisis that has overwhelmed this small country and severely taxed the ability of the government and aid organizations.

Lebanon now has the highest concentration of refugees as a percentage of population in the world, with about one Syrian for every three Lebanese. And new refugees keep coming as the civil war, which by some estimates has left more than 150,000 people dead, grinds into its fourth year. Each day, the United Nations registers 2,500 refugees in Lebanon, equivalent to more than one person per minute.

“The influx of a million refugees would be massive in any country. For Lebanon, a small nation beset by internal difficulties, the impact is staggering,” António Guterres, United Nations high commissioner for refugees, said in announcing the new number in a joint statement with Lebanon’s minister of social affairs, Rachid Derbas. “The Lebanese people have shown striking generosity, but are struggling to cope.”

Mr. Derbas called the breached threshold of one million “an occasion to launch a humanitarian and political call under the title: ‘Lebanon should not be left alone.' ”