CHICAGO (CBS) — House Republicans are moving forward with two immigration bills aimed at keeping families together after illegal border crossings.

The push for legislation comes a day after President Donald Trump signed an executive order halting his administration’s practice of separating migrant families for 20 days.

The president’s order keeps in place the administration’s “zero tolerance” policy of prosecuting every adult caught crossing the border illegally, and does not directly address the fates of the more than 2,300 children already separated from their families when their parents were prosecuted.

“It’s about keeping families together while at the same time being sure that we have a very powerful, very strong border,” Trump said Wednesday before signing the order.

While the Trump administration will halt the practice of separating migrant children from their parents at the Mexico border, the president’s order is effective for only 20 days. After that, kids might once again be split from their parents.

U.S. Sen. Dick Durbin (D-Illinois) said the president’s actions fall short.

“I read it closely, I read it carefully, and I will tell you this executive order by this president does not solve the crisis that he created,” he said on the Senate Floor on Wednesday.

House Republicans have been trying to negotiate immigration legislation that would keep families together throughout the length of any immigration proceedings. Two different proposals could be called for House Floor votes on Thursday.

The Republican measures would not end the “zero tolerance” policy on illegal border crossings, but would keep children with their parents in government custody while the adults are prosecuted.

A bipartisan group of senators also has said they are working on a long-term solution, including doubling the number of immigration judges to expedite asylum claims. However, questions remain about whether the government would detain families while prosecuting adults, or allow families to be released while moving forward with prosecutions for crossing the border illegally.

Trump’s about-face on the family separation policy came after mounting pressure from all sides.

“Ivanka feels very strongly. My wife feels very strongly about it,” Trump said.

The president rallied supporters in Minnesota on Wednesday night, hours after reversing course on separating children and parents at the border.

“We’re going to keep families together, but the border is going to be just as tough,” he said. “We want them to come in through the merit system, not a system where we get MS-13.”

A statement from the Department of Health and Human Services, which is in charge of taking in migrant children separated from their parents, said border agents are waiting guidance about what to do with children already split from their families.

Karen Freeman-Wilson, mayor of Gary, Indiana, flew to Texas on Wednesday to tour one of the child detainment facilities.

“Mayors are concerned. Certainly we don’t have the ability to enact federal policy, but we’re concerned because we are the elected officials who are closest to the people; who talk to them every day,” she said. “Even though I don’t have a child that was taken away from me, this has kept me up at night, and I’m sure I’m not the only one.”

Lauren Victory