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President Biden on Tuesday pledged to get the situation at the border "under control" as his administration faces a fresh border crisis in Del Rio, where more than 10,000 migrants have descended in recent days.

"We will get it under control," Biden said in response to a question about the border, after speaking at the United Nations General Assembly.

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He was then asked if his administration has it under control or will get it under control.

"We will get it under control," he repeated.

Biden’s administration has been facing a surge in migration that has overwhelmed officials and capacity since taking office. In August there were more than 208,000 migrant encounters, the second month in a row where encounters have been above 200,000.

While the administration has been repeating its claim that the border is not open, and noting that a significant number of encounters result in a Title 42 expulsion, it has been facing accusations from Republicans of encouraging mass migration by rolling back Trump-era policies like the Migrant Protection Protocols (MPP)

More recently, it has been facing a surge in Haitian migrants in Del Rio, where more than 10,000 are currently gathered as they seek entry into the United States. A combination of reports of canceled deportation flights and the extension of Temporary Protected Status (TPS) to Haitians already in the country, as well as dire conditions and political instability in Haiti, has fueled the crisis. The number at one point at the border was over 14,000, and there are reports of tens of thousands more on the way.

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The Biden administration has said it is increasing the number of deportation flights to Haiti and surging resources to the area as part of a multi-pronged strategy to get the situation under control. 

However, while it is deporting most single adults via Title 42, it is processing most migrant families into the U.S., and will soon be barred from using Title 42 to deport migrant families after it lost  a legal challenge to the policy in a federal court.

On Monday, DHS Secretary Alejandro Mayorkas visited the area and issued a stern warning to migrants thinking of making the journey to the U.S.

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"If you come to the United States illegally, you will be returned. Your journey will not succeed and you will be endangering your life and your family’s lives," Mayorkas said. "This administration is committed to developing safe, orderly and humane pathways for migration. This is not the way to do it."

He also said that the belief that the border is open is "false."

Fox News' Bill Melugin and Ronn Blitzer contributed to this report.