Texas Governor Greg Abbott has vowed to defend and hire the horse-mounted Border Patrol agents who the Biden administration may fire amid the recent developments at the border.

Abbott noted that President Joe Biden and Department of Homeland Security Secretary Alejandro Mayorkas were "in dereliction of duty" as they have "abandoned any pretense" of guarding the sovereignty of either Texas or the U.S. with their open border policies.

"If they are at risk of losing their job (from) a president who is abandoning his duty to secure the border, you have a job in the state of Texas. I will hire you to help Texas secure our border," the Republican governor told "Fox News Sunday."

The Daily Wire reported that Abbott also said that Texas has implemented a policy where they would arrest and jail people who come in across the border for trespassing into areas in the state.

Abbott noted that the Biden administration is refusing to do its duty to enforce the country's laws, leaving Texas in no position other than to step up, The Hill reported.

The Texas governor said his move to add hundreds of state police officers to the border last week was when the illegal migration stopped. He noted that that's what the Biden administration could exactly do if they wanted to.

Biden has condemned the horse-mounted Border Patrol agents, who were caught in the images chasing and aggressively dispersing Haitian migrants in Del Rio, Texas.

The president noted that there would be consequences for those actions, which Abbott commented on, saying false claims had circulated about the situation.

The governor noted that the person who took the pictures said the "characterization that the Democrats made" about the agents "whipping" migrants was false, adding that the migrants "were simply maneuvering horses.

READ NEXT: Biden Administration Suspends Use of Horses by Border Patrol Agents Amid Outrage

Border Patrol Agents Blast Joe Biden

The Border Patrol agents were furious that Joe Biden threw them under the bus over the Haitian migrant fiasco.

They are particularly angry at the White House's quick judgment over the pictures of an agent swinging the reins of his horse while confronting the migrants, Daily Mail reported. It was first believed that the agent was whipping the migrant.

But that account has already been debunked, with the photographer saying that his image showed no such thing. A Border Patrol agent told Daily Mail that it was "outrageous" that Joe Biden would not give them the benefit of the doubt before talking about the issue.

"He should have supported us as Federal agents, especially in light of how abysmally he's handled the border crisis," the agent said.

A second agent noted that they do their job for the safety and security of their families and the nation. The agent added that just because the president "won't man up and accept responsibility for his actions doesn't mean we won't."

On Friday, Joe Biden said the way the agents used their horses was "horrible" and that "people will pay" for their actions. He added that what the border agents did was "wrong," and it sends the wrong message around the world and "at home."

Investigation Into the Treatment of Haitian Migrants by Border Patrol Agents

Alejandro Mayorkas has promised an investigation into the treatment of Haitian migrants on the Texas border by agents on horseback, USA Today reported.

The DHS Secretary earlier told the House Homeland Security Committee that an undisclosed number of agents had been placed on administrative duty as investigators probe the situation that occurred in Del Rio.

Mayorkas said the investigation would be completed in days and not weeks. The DHS Office of Professional Responsibility will handle the examination, and the agency's inspector general has been notified.

READ MORE: Pres. Joe Biden's Administration Begins Deporting Haitian Migrants Staying Under Del Rio Bridge in Texas 

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Written by: Mary Webber

WATCH: Joe Biden Weighs in on Border Patrol Agents' Mistreatment of Haitian Migrants - From CBS Mornings