Immigration and Customs Enforcement (ICE) is weighing its options regarding arresting and deporting entire migrant families who have been ordered to leave the U.S., acting Director Mark Morgan reportedly said Tuesday.

Amid an influx of migrants crossing the border, the Department of Homeland Security has said it has had to prioritize deporting those it considers most dangerous, and the proposal would target migrants subject to a “final order of removal,” according to Morgan.

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"I think we can't exempt anybody," Morgan told reporters at ICE headquarters in Washington, according to CNN. "That will include families."

The proposed deportation efforts, Morgan said, would seek to discourage migrant families traveling to the U.S.

Due to restrictions on how long children can be held in custody, apprehended families are often released into the U.S. during legal proceedings. Families have made up the majority of border apprehensions in the steep increase, according to Customs and Border Protection data.

Morgan echoed President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE’s demands that the Mexican government immediately take action to reduce border crossings, saying the nation needs to “get off the sidelines.”

"They have 150 miles of choke point and a couple of major roads that are choke points that they could easily interdict. We have 2,000 miles along the southwest border," Morgan said. Trump has threatened to impose tariffs of 5 percent on Mexican goods beginning on June 10, with the percentage set to gradually increase until Mexico addresses border security to the administration’s satisfaction.

Morgan also said the administration is pushing for Mexico to become a “safe third country,” which the United Nations defines as a nation where refugees can seek asylum without danger. The majority of the recent influx of migrants have been Central Americans who pass through Mexico on their way to its northern border with the U.S.

Making Mexico a safe third country, Morgan said, would "really mandate Mexico to step up and really do more of what I believe they should be doing."