President Biden is expected to sign an executive order on Tuesday allowing him to temporarily seal the U.S. border with Mexico to migrants when crossings surge, a move that would suspend longtime protections for asylum seekers in the United States.

Mr. Biden’s senior aides have told members of Congress in recent days to expect him to sign the order at the White House alongside mayors from South Texas, according to several people familiar with the plans.

The restrictions would kick in once the number of illegal crossings exceeds 2,500 in a day, according to several people who have been briefed on the order. Daily totals already exceed that number, which means that Mr. Biden’s executive order could go into effect immediately.

The border would re-open to asylum seekers if the number of crossings stays below 1,500 for a certain period of time, the people said. They asked for anonymity because the executive order has not been officially announced.

The order would be the most restrictive border policy instituted by Mr. Biden, or any other modern Democrat, and echoes an effort in 2018 by President Donald J. Trump to curb migration that Democrats assailed and federal courts blocked.

Although the executive action is almost certain to face legal challenges, Mr. Biden is under intense political pressure to address illegal immigration, a top concern of voters before the presidential election in November.