The US government is offering migrants who are in the country illegally a sum worth $1,000 (£751) and paid travel if they decide to leave the US.
"Self-deportation is the best, safest and most cost-effective way to leave the United States to avoid arrest," Homeland Security Secretary Kristi Noem said in Monday's announcement.
Those who take up the offer could one day be offered a legal pathway to return to the US, Trump told reporters the same day.
Since returning to office in January, the president has launched a major crackdown on illegal immigration - at times relying on controversial tactics such as the invocation of a centuries-old wartime law. Some moves have faced legal challenges.
Those who signed up for the "self-deportation" financial incentive would not be prioritised for detention by immigration officials, the Department of Homeland Security (DHS) said in a news release.
The DHS said a first "illegal alien" had already taken up the offer, receiving a ticket for a flight from Chicago to Honduras.
The scheme relies on migrants utilising the CBP Home app, which can be used to confirm that person's return to their home country, officials explained in their release.
They described the offer as a "dignified" route, adding that it would cut the cost of deportations for the DHS. The average cost to arrest, detain, and deport a migrant currently stood at more than $17,000, they said.
Trump himself said the question of whether any given migrant would one day be offered a legal route back to the US was one of national interest.
"We're going to work with them so that maybe someday, with a little work, they can come back in if they're good people, if they're the kind of people that we want in our [country]," he told reporters.
The plan has also faced criticism. Adriano Espaillat, a Dominican-American congressman for the Democratic Party, wrote on X: "We don't bribe people to leave. We build a country where everyone belongs."
The president and his allies have touted their track record on immigration after three months in office, highlighting the fact that illegal crossings have dropped.
Border Patrol data showed a record low of just over 7,000 arrests at the US-Mexico border during the month of March.
Trump has also used an increase in detentions inside the country by Immigration and Customs Enforcement (ICE) to argue that his plan is working.
On the other hand, the administration has so far not managed to deport as many migrants as promised, and courts have blocked Trump's attempts to end birthright citizenship for certain children.
BBC