President Obama addresses the U.N. General Assembly. EPA/JUSTIN LANE

President Obama convened a special summit of world leaders in New York on Tuesday to address the dramatic increase in refugees across the globe, which he called "one of the most urgent tests of our time." History, he added, "will judge us harshly if we do not rise to this moment."

Among the nations the president thanked for its efforts was Mexico, which, Obama noted, "is absorbing a great number of refugees from Central America."

Yet human rights advocates have sharply criticized the Obama administration for its policy of deterrence when it comes to refugees from Guatemala, El Salvador and Honduras.

Despite clear warning signs, the administration was caught flat-footed in 2014 when tens of thousands of women and children from those nations surged across the U.S. border with Mexico, overwhelming Border Patrol stations in the Rio Grande Valley in Texas. Human rights advocates said the Central Americans were fleeing escalating violence and persecution perpetrated by drug cartels and organized crime in their home countries.

The administration responded to the mounting humanitarian crisis, and political embarrassment, with a multipronged strategy aimed at stemming the flow by making clear that the undocumented immigrants were not welcome in the United States and would be sent home if they did not win political asylum protections from an immigration judge.

In addition, Congress, with White House support, approved $750 million in development aid for the region, and the administration broadcast advertisements imploring would-be migrants to stay put. Obama and Vice President Biden pressured Mexican President Enrique Peña Nieto to tighten his country's borders with its neighbors and intercept those who made the journey north under the guidance of human smugglers.

The White House explained the policy by noting the dangers of the journey for women and children, some of whom were raped and abused along the way.

But advocates charge that the policy has not worked. The number of unaccompanied children who crossed the Mexican border illegally in 2014 was 68,000; the figure fell to 40,000 in 2015 but has swelled again to 54,000 this year, according to government statistics.

"The reasons for that are quite simple: The root causes of migration have continued unabated — violence in the region, narco-trafficking," Wendy Young, president of Kids in Need of Defense, said Tuesday during a conference in New York sponsored by the Center for Migration Studies.

The vast majority of Central American migrants who have arrived since 2014 are still in the United States, many in temporary shelters or family detention centers, awaiting their court hearings. The administration's policy remains that those who do not win asylum protections are eligible for deportation; in January, the Department of Homeland Security initiated raids in several cities to apprehend dozens of Central Americans with outstanding deportation orders.

Under mounting pressure from advocates, however, the administration announced plans this summer to expand a State Department program launched in 2014 that allows Central Americans to apply for refugee status in the United States from within their home countries. The administration also won a commitment from Costa Rica to accept 200 Central American minors who are in grave danger while their cases are examined by U.S. officials.

So far, only a few thousand children have won refugee status under the new programs.

"If you look at displacement around the world, there are more and more situations where nongovernment actors are the sources of violence," Young said. "It may not fit the classic perception of what a refugee is, but it's the same kind of abuse and the same levels of abuse we need to be aware of and offer safe haven to."

At his summit, Obama said nations have pledged to accept 360,000 refugees this year, twice as many as last year, and the private sector has promised $650 million in financial aid. But the cause is far bigger: A record 65 million people have been forcibly displaced from their homes, including 21 million who have left their home countries, according to the U.N. Human Rights Commission. Three million of them are awaiting asylum decisions, the study found.