“There is an investigation that the president certainly supports overseen by the Department of Homeland Security which he has conveyed will happen quickly. I can also convey to you that the Secretary also conveyed to civil rights leaders earlier this morning that we would no longer be using horses in Del Rio. So that is something, a policy change, that has been made in response," she said.
The images led Vice President Kamala Harris on Wednesday to "raise grave concerns" in a call with DHS Secretary Alejandro Mayorkas, her spokesman said.
Ms Psaki said the agents have been put on administrative leave while the incident is investigated.
She also denied reports that the White House would be sending migrants from the US southern border to Guantanamo.
"There's never been a plan to do that," Ms Psaki said.
'I will not be associated with it'
Meanwhile, the US special envoy to Haiti resigned in protest in a letter that blasted the Biden administration for deporting hundreds of migrants back to the crisis-engulfed Caribbean nation.
Daniel Foote, a career diplomat named to his post in July, said conditions in Haiti were so bad that US officials were confined to secure compounds. He said the "collapsed state" was unable to support the infusion of returning migrants.
"I will not be associated with the United States' inhumane, counterproductive decision to deport thousands of Haitian refugees and illegal immigrants," Mr Foote said in a letter addressed to Secretary of State Antony Blinken that circulated publicly on Thursday.
Haiti, the poorest nation in the Western Hemisphere, has been badly hit in recent weeks by a presidential assassination, gang violence and a major earthquake.
Mr Foote submitted his resignation to Mr Blinken on Wednesday, a State Department spokesperson said, adding that Washington was committed to the long-term wellbeing of Haiti, as well as offering immediate help to returning migrants.
State Department spokesman Ned Price rejected Mr Foote's criticism.
"This is a challenging moment that requires leadership. It is unfortunate that, instead of participating in a solutions-oriented policy process, Special Envoy Foote has both resigned and mischaracterized the circumstances of his resignation."
"He failed to take advantage of ample opportunity to raise concerns about migration during his tenure and chose to resign instead," said Mr Price.
The US government is continuing to fly hundreds of people back to Haiti, while releasing some into the US.
The US has returned more than 1,400 migrants from the camp in Del Rio, Texas to Haiti - including families - and moved over 3,200 people for processing away from the encampment.