Migrants said food remained scarce and there were not enough portable toilets.
Mexico and the United States were on Wednesday preparing to fly more Haitian migrants away from the camps.
At its peak, there were as many as 14,000 people camped out under the international bridge in Del Rio but US authorities have moved thousands away for immigration processing and deported more than 500 Haitians since Sunday.
The deportation flights to Haiti would continue, the US Department of Homeland Security (DHS) said.
Some Haitians have been released into the United States and allowed to pursue their immigration cases, according to media reports.
The DHS and US Customs and Border Protection did not respond to request for comment on the releases and did not say how it was decided who would be expelled and who would be released.
On Wednesday morning, a trickle of people - mostly men - crossed back into Mexico across the Rio Grande in search of food while a line of US border patrol cars on the upper banks of the river stood by.
Some have decided to stay on the Mexico side in Ciudad Acuna, across from Del Rio, because of shortages of food and poor conditions on the US side.
By Wednesday, about 200 people had set up a handful of camping tents and tarps as shelter.
One family was constructing a hut out of cardboard boxes.
A line formed outside a Doctors Without Borders truck hoping to get medical consultations, with one woman worried about her seven-year-old son with a cough.
US politicians from both parties have criticised Mr Biden's handling of the situation.
Authorities have ordered an investigation into an incident over the weekend in which mounted US border agents appeared to use reins like whips to intimidate migrants trying to cross the river.
Photographs and video of the agents on horseback sparked widespread condemnation.
DHS Secretary Alejandro Mayorkas said the agents involved had been pulled from front-line duties.
The expulsion flights to Haiti have also faced criticism.
There is profound instability in the Caribbean country, the poorest in the western hemisphere, where a presidential assassination, rising gang violence and a major earthquake have spread chaos in recent weeks.
Filippo Grandi, the head of the UN refugee agency, has warned that expulsions to such a volatile situation might violate international law.
Most of the Haitians have not arrived direct from Haiti.
Many had previously tried to settle in South America but recounted difficulties finding work amid pandemic-related restrictions and the economic downturn.