They said the Catholic Church will continue to "serve, accompany and assist" all those who flee persecution, "regardless of where they seek such protection and where they are from."
President Trump's order was part of a response to the several migrant caravans reported to be headed to the U.S. from Central America. It was intended to last for 90 days unless Mexico agrees to allow U.S. immigration officials to deport to Mexico those Central Americans who have entered the U.S. at the southern border.
"We need people in our country, but they have to come in legally," he said Nov. 9
According to DHS estimates, about 70,000 people a year claim asylum after crossing the border without documentation.
Recently media attention and immigration restriction advocates have focused on caravans of refugees and immigrants, sometimes growing or shrinking as they progress towards the U.S. border on a journey that can be dangerous.
The latest caravan of about 3,000 people has arrived in Tijuana, across the U.S.-Mexico border from San Diego. U.S. Border and Custom Protection officials said they closed northbound traffic at the San Ysidro crossing for several hours on Monday to install movable barriers in response to reports that there was a plan to rush the crossing. There was no rush, the Associated Press reports.
On Nov. 9 President Trump had said that the situation of people crossing the southern border has changed in recent decades. About two decades ago, the average person caught crossing the southern border was a single adult who was immediately returned to Mexico, and did not try to claim asylum or express fear about going back to their country of origin.
He claimed there has been a "massive increase" in fear-of-persecution or torture claims. While the "vast majority" satisfy the first asylum step of appearing to have a credible fear, only a "fraction" are ruled to qualify for asylum.
There are about 1.1. million asylum cases pending in immigration courts, and about 20 percent of applications for asylum are approved, the Associated Press reports.
Other officials who defended the new policy have said it would encourage migrants to pass through official border crossings where their asylum claims can find a fast hearing. The border is close to 2,000 miles long.
Between the active date of President Trump's order and the court ruling, DHS had referred over 100 people who had sought asylum without going to an official crossing to U.S. Citizenship and Immigration Services.
(Story continues below)
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The president has advocated revoking the right to citizenship of babies who are born in the U.S. to non-U.S. citizens. His family separation policy came under strong criticism and was changed.
His travel ban on foreigners from several predominantly Muslim countries was blocked in federal court before the U.S. Supreme Court let it stand.
Most of his immigration actions have come through regulatory change and presidential orders, rather than through new legislation passed by Congress.