As President Biden considers sweeping changes to the American asylum system, his administration took smaller steps this week to try to control the system’s notorious backlogs.

On Thursday, the administration proposed a rule change that would allow officers to quickly identify people who are ineligible for asylum, such as those who have been convicted of serious crimes.

The goal of the proposal, which must go through a 30-day public comment period, is to remove ineligible people from the United States soon after they cross the border, rather than allowing them to wait months, or often years, for asylum proceedings.

Also Thursday, the U.S. Citizenship and Immigration Services issued a new policy instructing asylum officers to consider whether applicants could have found refuge in their own countries before coming to the United States.

The information could then be used to determine whether the applicants should pass their initial asylum screening, according to a notice that went out to officers. That change is set to take effect on May 17.

Neither announcement is expected to have a major effect on a chronically underfunded and understaffed asylum system. The rule to speed up processing, in particular, would apply only to a small number of applications deemed to be national security threats.

But the moves show the Biden administration’s focus on securing the border as migration remains a dominant concern for voters ahead of the presidential election.

Mr. Biden has taken a much harder line on immigration as the number of people crossing the U.S.-Mexico border has reached record levels over the course of his presidency.

He has even considered executive action that could prevent people who cross illegally into the United States from claiming asylum, a move that would suspend longtime guarantees that give anyone who steps onto U.S. soil the right to ask for safe haven.

“There’s no guarantee that I have that power all by myself without legislation,” Mr. Biden said in April. “And some have suggested I should just go ahead and try it. And if I get shut down by the court, I get shut down by the court.”

In recent months, however, numbers at the border have gone down dramatically from where they were in December, when border agents made more than 250,000 arrests. The numbers have dropped each month, and the count is expected to be even lower for April, at around 129,000.