The number of migrants crossing the southern border has dropped sharply since the Biden administration imposed severe restrictions on asylum last month.

In June, just over 83,000 migrants crossed the border illegally, according to U.S. border officials, down from around 117,000 in May and the lowest monthly total since January 2021.

The downturn in crossings has continued into July. The daily average of encounters at the border in the past week was under 1,900 as of Monday, according a senior U.S. Customs and Border Protection official, who spoke on the condition of anonymity to discuss internal statistics.

The steep decrease coincides with the implementation of a June policy that bans asylum at the southern border, along with ramped-up enforcement from Mexican officials starting this year.

But it comes at a time when the country’s attention is focused on the questions surrounding the continued candidacy of President Biden in this year’s presidential election and the attempted assassination of former President Donald J. Trump. The political benefits of a border crackdown may yet prove fleeting.

And as a harsher view of illegal immigration has taken hold among many Americans, surveys suggest Mr. Trump’s harder line may resonate more with swing voters, including some Hispanic Americans.