President Joe Biden is expected to sign an executive order on immigration as early as this week, according to sources familiar with the decision.

       The long-awaited executive order would limit the number of migrants that would be allowed to claim asylum at the southern U.S. border. It would immediately send them back to their country of origin to wait until the daily average goes down and, once it goes down, they would be able to claim asylum, according to a source familiar.

       The daily number of encounters has to hit 2,500 for the provision to kick in, according to sources briefed on the situation, meaning that one day of more than 2,500 migrants would trigger the provision of limiting asylum at the border.

       In recent days, members of Congress have been briefed on the executive action, according to sources familiar with the briefings.

       MORE: Biden administration aims to expedite migrant asylum claims from years to months

       Any executive order, administration officials caution, would be challenged in court.

       "I anticipate that if the president would take executive action, and whatever that executive action would entail, it will be challenged in the court," Homeland Security Secretary Alejandro Mayorkas told reporters last month at Department of Homeland Security headquarters.

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       Mayorkas and other members of the administration have urged Congress to pass the bipartisan border bill that was negotiated and proposed earlier this year.

       MORE: Unaccompanied minors are representing themselves in immigration court, alarming advocates

       A spokesperson for Brownsville, Texas, Mayor John Cowen confirmed to ABC News that the White House invited him to a meeting at the White House on Tuesday for an immigration-related announcement, and he will be attending.

       El Paso Mayor Oscar Leeser also confirmed he is attending. He told ABC News in a statement: "El Paso is a welcoming community, and that makes me very proud, but no community can continue the effort and resources we've expended on this humanitarian crisis endlessly. We are appreciative of the funding we have received from the federal government so that our efforts don't fall on the backs of El Paso taxpayers, but our immigration system is broken, and it is critical that Congress work on a bipartisan long-term plan to work with other countries in order to create a more manageable, humane and sustainable immigration system for our country.

       "I look forward to hearing more about the president's plan on Tuesday, and we stand ready to work with our partners at the local, state and federal level on this effort," he added.

       ABC News' Armando García contributed to this report.