President Biden issued an executive order on Tuesday that temporarily prevents migrants from seeking asylum at the U.S.-Mexico border when crossings surge, seeking to ease pressure on the country’s immigration system and address a major concern among voters.

The dramatic election-year move is 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 cut off migration that was blocked in federal court.

The restrictions kick in once the seven-day average for daily crossings hits 2,500. Daily totals already exceed that number, which means that Mr. Biden’s executive order could go into effect right away, allowing border officers to return migrants across the border into Mexico or to their home countries within hours or days.

The border would reopen to asylum seekers only when the number of crossings falls significantly. The figure would have to stay below a daily average of 1,500 for seven days in a row. The border would reopen to migrants two weeks after that.

White House officials expect the order will be challenged in court. Still, the move shows how drastically immigration politics have shifted in the United States. Polls suggest there is support in both parties for border measures once denounced by Democrats and championed by Mr. Trump as the number of people crossing into the country has reached record levels.

There would be limited exceptions, including for minors who cross the border alone, victims of human trafficking and those who use a Customs and Border Protection app to schedule an appointment with a border officer to request asylum.