Many of the thousands have been released into the country with notices to appear at an immigration court within 60 days, one source told the AP.
The Homeland Security Department has been busing Haitians from Del Rio to El Paso, Laredo and Rio Grande Valley along the Texas border, and this week added flights to Tucson, Ariz., the official said. They are processed by the Border Patrol at those locations.
Expulsion flights back to Haiti started on Sunday and more than 500 have been removed, according to Reuters.
The officials spoke on the condition of anonymity because they weren’t authorized to discuss the matter.
Back in Port-au-Prince, many of the deported Haitians expressed their anger and some migrants tried unsuccessfully to get back on a plane returning to the U.S., according to Reuters.
"I am angry at the [Haitian] government," Yranese Melidor, another deported migrant, told Reuters. "We were told …that the Haitian government had signed to send us back to Haiti. They are all bad people, these authorities."
The head of the U.N refugee agency said the expulsions might violate international law by sending refugees back to life-threatening situations, and Senate Majority Leader Chuck Schumer said the deportations "defy common sense," Reuters reported.
DHS confirmed to Fox News Tuesday that three U.S. Immigration and Customs Enforcement officers were injured after "two separate disruptions" by Haitian migrants when they deplaned on the tarmac at Port-au-Prince. The injuries were not life-threatening.
"On Tuesday, Sept. 21, some adult migrants caused two separate disruptions on the tarmac after deplaning in Port-au-Prince, Haiti," a DHS spokesperson said. "Haitian crowd control officers responded to both incidents and resolved the situations. ICE fully respects the rights of all people to peacefully express their opinions, while continuing to perform its immigration enforcement mission consistent with our priorities, federal law and agency policy."
U.S. Sen. Jon Ossoff, D-Ga., questioned Department of Homeland Security (DHS) Secretary Alejandro Mayorkas on DHS' sluggish response time during a Tuesday Senate Homeland Security Committee hearing on "Threats to the U.S."
Mayorkas responded that Ossoff’s concern was "resonant" and that DHS has "done an internal review on the pace" of its responsiveness as well as "implemented new procedures" to decrease response time.
Ossoff had joined a number of Republicans on the committee in hammering Mayorkas on the backlog of requests to the department.
Mayorkas had visited the migrant camp on Monday.
U.S. Customs and Border Protection didn't immediately respond to Fox News' request for confirmation.
A Department of Homeland Security spokesperson told Fox News: "DHS continues to expel migrants under CDC’s Title 42 authority. Those who cannot be expelled under Title 42 and do not have a legal basis to remain are placed in expedited or full removal proceedings.
Individuals who are not immediately repatriated are either placed in Alternatives to Detention, detained in an ICE facility, or released with a legal document (either a Notice to Appear in court or a notice to report to an ICE office for further immigration processing). The document an individual receives is dependent on facility space and resources available to process.
As part of the process, Border Patrol agents collect biometric and biographic information – fingerprints, photos, phone numbers, and an address in the United States – and run a background check to identify criminals or those who pose a public safety risk. Those who do not report, like anyone who is in our country without legal status, are subject to removal by ICE.
The Biden Administration has reiterated that our borders are not open, and people should not make the dangerous journey. Individuals and families are subject to border restrictions, including expulsion. Irregular migration poses a significant threat to the health and welfare of border communities and to the lives of migrants themselves, and should not be attempted."
Fox News' Adam Shaw and Houston Keene and the Associated Press contributed to this report.