The approximately 1,800 migrants are housed by the Mexican government on the Rio Grande in Piedras Negras.
Central American immigrants want to come to the US, but the US authorities are asking them to stay in Mexico while awaiting asylum.
The migrants turned up on Monday and arrived at the border as 50 buses.
In preparation for the arrival of the migrants, Texas Republican Governor Greg Abbott sent 500 officers from the Public Security Department to Eagle Pass, said Mayor Ramsey English Cantu.
A CNN crew there Thursday night saw the Public Security Department along with border patrol vehicles near the river banks with emergency lights on.
"As part of our border security plan, we keep DPS on the edge of boats and planes, and work with local and federal authorities to enforce the law," tweets Abbott.
The Department of Public Safety declined to comment and said it was not about safety issues.
"That said, DPS continues to provide direct support to our local, state, and state partners, including the US Border Guard, to increase border security and drug and human smuggling to Texas and the nation fight, "it said in a statement.
The US military is also sending 250 active troops into the city, the Pentagon said Wednesday. These include military police, medical personnel and engineers responsible for setting up razor wire.
The migrants live in an old warehouse that has been converted into a shelter.
Every day, 16 to 20 cases can be processed, said Paul Del Rincon, Port Director of the Eagle Pass Port of Entry.
According to the US census, the Eagle Pass has about 26,000 inhabitants.