President Donald Trump first announced the trip by his wife, who was touring a non-profit social services center for migrant children, before heading to a customs and border patrol processing center, according to a statement from her office.
First lady Melania Trump made a surprise visit to a McAllen detention center that is housing some of the children.
New York Mayor Bill de Blasio said separated immigrant children still don't know when they will see their parents again.
Despite Trump's executive order, a host of unanswered questions remain, including what will happens to the children who were already separated from their parents and where the government will house all the newly detained migrants, with the system already bursting at the seams.
The first lady commented in a written statement Thursday after she returned from touring the Upbring New Hope Children's Center in McAllen, Texas.
The group was denied immediate access to a holding facility by the Department of Health and Human Services, said Steve Benjamin, mayor of Columbia, South Carolina.
Wednesday, President Trump signed an executive order ending the policy of separating immigrant families who cross the border illegally.
Mr Trump said yesterday as he signed an order to scrap the policy: "It's about keeping families together while at the same time making sure that we have a very powerful, very strong border". "And I also like to ask you how I can help to these children to reunite with their families as quickly as possible".
Trump signed an executive order requiring immigrant families be detained together when they are caught entering the country illegally for as long as their criminal proceedings take.
"We have a chance", US Representative Carlos Curbelo said. Children can not follow their family members or guardians into custody, so United States guidelines mandate that those children be separated - often from their parents.
The separations were enacted as part of Trump's zero-tolerance immigration policy, which holds that any adult crossing the border illegally will be criminally prosecuted. "On the other hand, we shouldn't be doing it unless we have all the structures in place to accommodate the families right away".
When Mrs. Trump visited, the kids were in the middle of classes.
The former model arrived in a casual outfit - an apt choice that included warm hues seen in her light safari top, white pants and white Adidas Stan Smith sneakers.
Asked about it, her spokeswoman Stephanie Grisham said: "It's a jacket".
Speaking at a Cabinet meeting shortly after the first lady arrived at the facility, the president said of the separations, "it really bothered her to be looking at this and seeing it".