CIUDAD ACUNA, Mexico, Sept 21 (Reuters) - U.S. President Joe Biden faced bipartisan anger on Tuesday over the handling of an impromptu, mainly Haitian, migrant border camp in Texas, with Republicans saying security was lax and Democrats worried about the humanitarian situation.

The conflicting demands underscored policy challenges the Biden administration faces as it tries to manage record numbers of border arrivals this year that Republican Senator Mitt Romney on Tuesday called a "disaster."

Republican politicians with an eye on 2022 midterm elections have been quick to portray the sprawling camp of some 10,000 people in the shadow of a bridge over the Rio Grande as the result of Democrats' push to end some migration restrictions.

Texas Governor Greg Abbott said a shallow point across the river was an obvious place to reinforce the border with more guards to prevent people reaching U.S. territory.

However, U.S. Senate Majority Leader Chuck Schumer also ramped up the pressure on Tuesday, saying it "defies common sense" to expel the migrants to Haiti, and expressing anger over tactics used by border guards to control the crowds.

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Several United Nations agencies also voiced concerns about the deportation of migrants to Haiti, citing instability in the poor Caribbean nation, where a presidential assassination, rising gang violence and a major earthquake have spread chaos in recent weeks.

The U.N.'s refugee agency said expulsions without screening for protection needs were "summary," "inconsistent with international norms and may constitute refoulement."

U.S. Vice President Kamala Harris said the situation was complex and that the United States needed "to do a lot more" to support the basic needs of people in Haiti.

"People want to stay home, they don't want to leave home, but they leave when they cannot satisfy their basic needs," she told reporters.

Several hundred have already been sent to Haiti from the camp in Del Rio, Texas, since Sunday. Thousands more have been moved into U.S. detention for processing and more flights are slated. One arrived in Haiti on Tuesday.

The camp's population peaked at up to 14,000 at the weekend, but has since diminished.

In Texas, three Haitians briefly escaped from a bus traveling towards Brownsville on Monday, according to Jaime Garza, chief deputy at the Kleberg County Sheriff's Office. The bus was one of two transporting Haitian migrants from the border, he said.

The three escaped and ran, but were immediately apprehended, he said.

Mexican authorities also detained some Haitians, who have regularly crossed from Del Rio back over to Mexico to get food.

A Reuters crew witnessed one encounter, where several migrants yelled and protested as Mexican agents boarded them into a National Immigration Institute (INM) van. INM did not immediately respond to a requests for comment.

'Helping greatly'

A new camp has been growing on the Mexican side, where migrants were aided by groups including the Red Cross and Doctors Without Borders, as well as the U.N's migration agency.

Residents from Ciudad Acuna brought food to the migrants.

Surreane Petit, who clutched her 3-year-old boy at her side, said staying in Mexico was a huge improvement over the U.S. camp. "Here the Mexican people are helping greatly."

"Over there we were hungry," Petit said. "Under the bridge there was no help, no help."

She said she had lived the last five years in Chile, where her son was born, but decided to leave after pandemic lockdowns made it hard to leave her house to find work.

Following an outpouring of anger over an incident in which mounted U.S. border agents in cowboy hats used horse reins like whips to intimidate the migrants, U.S. Department of Homeland Security Secretary Alejandro Mayorkas emphasized that U.S. border agents were delivering medical attention and were working with the Red Cross.

Mayorkas said he was horrified by the images of the mistreatment, echoing increasingly strident criticism from the White House which said the footage "does not represent who we are as a country."

Despite the risk of being returned to Haiti, many migrants remained in the Del Rio camp.

Carly Pierre, 40, said he was staying in the U.S. camp because he saw a chance to make it into the United States with his wife and two children, ages 3 and 5, after several years living in Brazil.

"There are deportees, and there are people who will make it in," he said, shorts still wet from having crossed the river to buy ice and soda at a convenience store on the Mexican side.

(Reporting by Daina Beth Solomon in Ciudad Acuna; Additional reporting by Doina Chiacu in Washington, Kristina Cooke in San Francisco, Mica Rosenberg in New York, and Stephanie Nebehay in Geneva; Writing by Frank Jack Daniel; Editing by Bernadette Baum and Rosalba O'Brien)