The Central American migrants pouring across the Southern border pose a different but no less challenging problem. Individuals who enter the United States illegally do not necessarily qualify as refugees, although a growing proportion of Central Americans are arriving with claims of asylum, asserting that they are seeking refuge from violence and mortal threats in their home countries.

While administration officials say they are working to address the root causes of the migration and to set up new programs to extend humanitarian protection to those who need it, their primary response has been to try to deter Central Americans from making the dangerous journey to the United States. One method has been to deport those whose asylum claims have been rejected.

“We have to control the border, that’s our job, and we have to honor our humanitarian obligation,” Cecilia Muñoz, the director of Mr. Obama’s Domestic Policy Council, said in an interview. “The situation in Central America, as terrible as it is, the legal standard may not be fully up to addressing why people are leaving.”

Humanitarian groups have denounced the administration’s approach, arguing that the president must recognize the Central American migrants as refugees.

“The administration’s entire foreign policy has been built upon enforcement, not protection,” said Anna Greene, the director of policy and advocacy, United States programs, for the International Rescue Committee. “If this situation was playing out far from our borders, our government would be funding a humanitarian response and demanding that other countries abide by their international obligations.”

The criticism comes as some of Mr. Obama’s allies on Capitol Hill are arguing that he has not done enough to respond to the Syrian refugee crisis. Twenty-seven Democrats led by Senator Richard J. Durbin of Illinois, who was Mr. Obama’s partner in the Senate and maintains close ties with the president, told him in a letter this month that the administration “can and should do much more” to accept Syrian refugees.