Migrants from Central America walk on a highway during their journey towards the United States, in Ciudad Hidalgo, Chiapas state, Mexico, June 5, 2019.

The Trump administration is proposing a new rule that would deny asylum to migrants who have been convicted of misdemeanors like possession of marijuana.

The Justice Department and Department of Homeland Security propose in a draft of the rule, which was published Thursday in the Federal Register, to expand regulations governing asylum eligibility and disqualify those convicted "for possession or trafficking of a controlled substance" from U.S. protections.

"Specifically, the departments propose that a conviction for possession or trafficking of a controlled substance or controlled-substance paraphernalia, other than a single offense involving possession for one's own use of 30 grams or less of marijuana, should disqualify an alien from eligibility for asylum," the notice said.

"Both possessors and traffickers of controlled substances pose a direct threat to the public health and safety interests of the United States, and they should not be entitled to the benefit of asylum," according to the description of the proposed rule change.

Convictions related to domestic violence could also make migrants ineligible, according to the notice.

The administration said it will have a 30-day comment period on the proposal before the law will likely take effect.

The White House did not immediately respond to request for comment.

According to the Homeland Security, 38,687 individuals were granted asylum as refugees in 2018. The leading countries were China, Venezuela, and El Salvador.

The proposal is just one of several actions from the Trump administration, which has pushed rules that exclude immigrants from entering or staying in the U.S. Current rules bar migrants seeking asylum who have been convicted of crimes like murder or rape.

In September, the Supreme Court allowed nationwide enforcement of a Trump administration rule that prevents most Central American immigrants from seeking asylum in the United States.The policy is meant to deny asylum to anyone who passes through another country on the way to the U.S. without seeking protection there first.

—The Associated Press contributed to this report.