President Donald Trump on Tuesday repeated his false claim that Democrats are solely responsible for his decision to separate migrant children from their parents when they attempt to illegally enter the United States.

“As a result of Democratic-supported loopholes in our federal laws, most illegal immigrant families and minors from Central America … cannot be detained together or released together, only released,” he said during remarks at a small-business conference in Washington, adding that the “crippling loopholes … cause family separation that we don’t want.”

[Trump Heads to Hill After Sowing Confusion on Immigration]

While the president has been using the line for the last week, his own Cabinet officials and senior aides have explained the policy’s genesis very differently,

Attorney General Jeff Sessions and White House domestic policy adviser Stephen Miller have boasted about their decision to prosecute all adults attempting to illegally cross the U.S.-Mexico border — even if they show up with children. Homeland Security Secretary Kirstjen Nielsen and others point to a 2008 child-trafficking law and a subsequent court ruling, saying both leave the administration with its hands “tied,” and compel law enforcement officials to send migrant children to one processing center and adults to another for the misdemeanor offense of crossing the border.

None of Trump’s senior aides have pinned the 2008 law — which passed both chambers unanimously and was signed by Republican President George W. Bush — like their boss has.

House Oversight and Government Reform ranking member Elijah E. Cummings pleaded with Republicans to deliver a message to the president later Tuesday when they will huddle with him in the Capitol basement to talk immigration.

“We need you to tell him we reject this mean policy. We need you to tell him to abandon this policy,” the Maryland Democrat said. “We need you to remind him this is the United States of America and it is a great country. And we need you to stand up for these children.”

Watch: Cummings Get Emotional About Separation Policy

Members of both parties want the administration to quickly end the practice of removing migrant children from their parents. Senate Majority Whip John Cornyn said Republicans are crafting legislation now.

“We’re going to present, after we get sort of buy-in from our Republican Conference, to our Democratic colleagues to say this is a simple, straightforward solution that doesn’t carry with it a lot of the baggage that usually drags down immigration reform,” the Texas Republican told reporters Tuesday.

[5 Things to Watch in House Immigration Debate This Week]

To that end, Trump signaled he wants Congress to send him a bill to address existing law and the court ruling that would allow his administration to keep migrant families together as parents await prosecution — notwithstanding the leeway law enforcement and prosecutors exercised before Sessions outlined the zero tolerance policy this spring.

But it is rarely that easy with Trump. For instance, Nielsen said Monday the administration would not accept a narrow fix, opting instead to push for a more sweeping immigration overhaul.

Meantime, the president uttered one more thing unlikely to prove true during Tuesday’s remarks to the small-business group. He said Republicans would vote together “100 percent” on any immigration measure.

Yet, both a conservative House measure and an accompanying GOP compromise bill are expected to fall short in the chamber, even though Republicans have enough votes to pass one or both without Democratic help. And when the Senate took up three immigration measures earlier this year, enough GOP senators voted against each one to sink them.

While just what substance Trump might accept on a bill to reverse family separation or on a broader immigration measure remains unclear, his desired fate for migrant families is clear. “We have to bring them back to their countries,” he said Tuesday, echoing hard-line West Wing staffers like Miller.

Trump said he expects to “make changes” to any immigration legislation the House might pass this week. He did not specify which alterations he has in mind. And he described his late-afternoon session with House Republicans as them briefing him on their two bills, even though he has staff for that.

Todd Ruger and Kellie Mejdrich contributed to this report.