(CNN) Customs and Border Protection Commissioner Kevin McAleenan said Wednesday that the "breaking point has arrived this week" for the US immigration system.

Speaking from El Paso, Texas, the head of the US border security agency said that on Monday, CBP encountered the highest total number of migrants in years, with more than 4,000 in a single day, the vast majority of which were apprehensions of people illegally crossing the border.

That number was broken again on Tuesday.

McAleenan said the agency is on pace to apprehend and encounter "over 100,000" migrants this month. Ninety percent of those are expected to be for illegal border crossings.

"March will be the highest month since 2008," he said.

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