WASHINGTON—President Trump advocated on Saturday for the controversial policy of separating families that cross into the U.S. illegally, saying that fear of being separated from children deters some immigrants.

Speaking to reporters at the White House, Mr. Trump warned that adults are using children to cross into the U.S. from Mexico.

“If they feel there will be separation, they don’t come,” he said. “You’ve got some really bad people out there.”

Attempts to increase deterrence—including the Trump administration’s controversial family separation policy that was abandoned in June—haven’t been effective in slowing the influx of families.

A record number of asylum-seeking families has overwhelmed border agents and immigration authorities. Border Patrol facilities are crowded with newly arrived families, bed space at family detention centers in Texas is at a premium and immigration court backlogs are growing.

Migrant children separated from their parents under the Trump administration’s “zero tolerance” policy frequently spent days in government facilities designed for short-term use as the Department of Homeland Security struggled to track and reunify families, according to a report released this month by the Department of Homeland Security’s Office of Inspector General.

Since children can’t be held in criminal custody, more than 2,000 children were separated from their parents at the border in May and June, prompting widespread criticism from members of both parties before Mr. Trump ultimately rolled back the policy at the end of June.

“Chain migration is bad,” Mr. Trump told reporters. “If you take a look at the lottery system, that’s bad.”

Mr. Trump reiterated his preference for a merit-based immigration system, saying “a vast majority of the country agrees.”

The president blamed Democrats for a lapse in legislation, saying they should have passed “good bills” and noted that former President Obama faced similar challenges.

“In the old days, when the country wasn’t doing well, it was allowed easier,” he said, adding that the current influx is “because of how well our country is doing.”

On Friday, the Washington Post reported that the White House is actively considering plans that could again separate parents and children at the U.S.-Mexico border.

At a rally in Kentucky late Saturday, Mr. Trump urged the crowd of supporters to elect Republicans, so he can pass legislation to end “Catch and Release”--the policy of releasing immigrants into the community while they await a hearing to determine their status.

“Lottery? Lottery?” he repeated to the sound of boos from the crowd. “These states that set up lotteries—do you really believe that they’re giving us their finest?”

Write to Vivian Salama at vivian.salama@wsj.com

Corrections & Amplifications

The Washington Post reported that the White House was considering a new policy of family separation. An earlier version of this article incorrectly stated that it was reported by the New York Times. (Oct. 13, 2018)