Senate Minority Leader Charles E. Schumer (D-N.Y.), alongside House Minority Leader Nancy Pelosi (D-Calif.), speaks with reporters outside the Capitol on June 26. (Aaron P. Bernstein/Getty Images)

A senior Trump administration official said Tuesday that it is up to Congress to fix President Trump’s migrant separation policy and ensure families are reunited, an argument rejected by Democrats who insist Trump created the problem and should solve it himself.

The back and forth on Capitol Hill underscored how unlikely it is a divided Congress will do anything to deal with the policy before lawmakers leave Washington for a 10-day Fourth of July recess. In the meantime, more than 2,000 migrant children remain in federal custody separated from their parents amid chaotic attempts to reunite them.

Republicans are struggling to pull together targeted legislation to address the legal implications of the policy during a public outcry five months before midterm elections with congressional majorities at stake.

Health and Human Services Secretary Alex Azar told senators at a hearing Tuesday that it was up to Congress to overturn a 21-year-old court settlement that prevents the federal government from detaining families together for more than 20 days.

“I cannot reunite them . . . while the parents are in custody because of the court order that doesn’t allow the kids to be with their parents for more than 20 days,” Azar told the Senate Finance Committee. “We need Congress to fix that.”

Draft GOP legislation would change existing law to allow the Department of Homeland Security to hold families together indefinitely in custody, extending a 20-day limit on child detentions established under a 1997 court settlement known as the Flores case.

One proposal endorsed by most Senate Republicans would move those families to the front of the line for adjudication, which, they say, would result in the families being deported or released into the United States within weeks.

But House Minority Leader Nancy Pelosi (D-Calif.) and Senate Minority Leader Charles E. Schumer (D-N.Y.) said that they could not endorse a GOP plan that would keep families in extended detention.

“Everybody in our caucus understands that the Flores decision is not improved by extending the length of time; it is weakened,” Pelosi said, calling it a “cynical attempt” by Republicans.

Schumer said it remains up to Trump, not Congress, to reverse the “zero tolerance” enforcement policy that has prompted the practice of separating migrant children from their parents at the border.

“The president created this problem,” Schumer told reporters. “The quickest way to fix it is administratively.”

House Republicans, meanwhile, have flailed in trying to pass broader immigration legislation, with Trump sending mixed signals over the past week — first telling GOP lawmakers to pass a bill, then telling them not to bother until after the midterm elections.

The president summed up his preferred immigration policy in a White House meeting Tuesday with GOP lawmakers: “It’s called, ‘I’m sorry, you can’t come in.’ ”

An executive order signed by Trump last week aimed to reverse some aspects of the policy, but it cannot undo the Flores requirement, and its execution has been otherwise confused.

The four main negotiators on a family separation bill — Sens. Dianne Feinstein (D-Calif.), Richard J. Durbin (D-Ill.), Ted Cruz (R-Tex.) and Thom Tillis (R-N.C.) — have discussed a potential measure that could pass the Senate but indicated it would have to wait until next month.

Tillis and Cruz said they would be open to the use of ankle bracelets or other remote monitoring to help track migrants and ensure they appear for court hearings. Tillis said that most asylum cases were handled in 30 to 60 days and that the parties needed to determine a reasonable maximum amount of time to keep families detained.

Durbin said he and Feinstein considered it “fundamental that we have protections for humane treatment for children who come to our borders” and that they oppose rolling back the Flores settlement.

At the Senate hearing Tuesday, Azar was repeatedly questioned about the unaccompanied children in his department’s custody. Indicating slow progress in reuniting separated families, Azar said 2,047 children remain in HHS care, only six fewer than last week.

Meanwhile, the House remains stuck in an immigration quagmire. A group of conservatives said Tuesday that days of last-ditch negotiations had failed to persuade them to support a broad immigration bill set for a vote Wednesday.

The bill would provide $25 billion for Trump’s long-sought border wall, give young undocumented immigrants a path to citizenship and impose limits on legal immigration.

The House had been set to vote on the broad bill last week, immediately after a more conservative bill failed to pass. But negotiators instead chose to work through the weekend to further hone the bill. Late Monday night, GOP leaders filed a 116-page amendment that would expand temporary visas for agricultural workers while also requiring all employers to screen their workers for legal status using the federal “E-Verify” database.

But many conservative hard-liners exiting a closed-door meeting of House Republicans on Tuesday morning said that the changes would not be enough to secure their votes. By Tuesday evening, House leaders had decided to abandon the amendment.

“I’m not in favor of additional amnesty,” said Rep. Jody Hice (R-Ga.), referring to a provision in the bill that would offer permanent legal status to as many as 1.8 million young undocumented “dreamers” who arrived in the United States as children. “E-Verify is important, I’m all for that, but I’m not for expanding the numbers.”

Ahead of likely defeat, House Speaker Paul D. Ryan (R-Wis.) appeared ready to move on.

“Ultimately we’re going to arrive on fixing this broken immigration system,” Ryan said. “Hopefully, it’s now. If not, it’s going to be later.”

Lawmakers and aides said the failure of the broader bill Wednesday would pave the way for consideration of a narrower bill focused solely on the family separation policy — and abandoning, for now, the pursuit of a far-reaching immigration overhaul.

Rep. Cathy McMorris Rodgers (R-Wash.), the No. 4 House Republican leader, is leading an effort to craft a narrow fix on the House side to be voted on this week, though she and other GOP leaders have been reluctant to discuss it while the broader bill is pending.

Colby Itkowitz, Sean Sullivan and John Wagner contributed to this report.