One option under consideration is for the government to detain asylum-seeking families together for up to 20 days, then give parents a choice — stay in family detention with their child for months or years as their immigration case proceeds, or allow children to be taken to a government shelter so other relatives or guardians can seek custody.

That option — called “binary choice” — is one of several under consideration amid the president’s frustration over border security. Trump has been unable to fulfill key promises to build a border wall and end what he calls “catch and release,” a process that began under past administrations in which most detained families are quickly freed to await immigration hearings. The number of migrant family members arrested and charged with illegally crossing the border jumped 38 percent in August and is now at a record level, according to Department of Homeland Security officials.

Senior administration officials say they are not planning to revive the chaotic forced separations carried out by the Trump administration in May and June that spawned an enormous political backlash and led to a court order to reunite families.