Pope Francis also joined the public outcry, telling Reuters he agreed with US Catholic bishops that separating children from their parents at the border was "immoral".
In theory, the intent of the executive order is to keep children who have crossed the border with their parents while in custody.
Trump said Wednesday he didn't like seeing children being removed from their families, a recent practice that has sparked worldwide outrage.
'When you prosecute the parents for coming in illegally, which should happen, you have to take the children away'. A source close to Trump added: "This was the biggest communications fail I've seen out of this White House, and that's really saying something".
After all, the entire exercise had been born out of a rebellion by House moderates who in May sought to use a rarely deployed procedural move, a discharge petition, that would have bypassed leadership and forced a vote on four different immigration bills.
But Republicans said they were uncertain if either measure would have enough support to be approved.
"Well, we're working with our members".
However, Republicans, who have a majority in both the upper and lower house, have signaled that they may not have sufficient votes to pass the legislation.
"It is still very early and we are awaiting further guidance on the matter", said Brian Marriott, senior director of communications at the Administration for Children and Families, a division of Health and Human Services. "What could possibly be the reason for that except to punish them?"
Separately, Attorney General Jeff Sessions met with Senate Republicans privately amid GOP fears about the political fallout from the separation policy. If those options are exhausted, authorities must find the "least restrictive" setting for the child who arrived without parents.
Delaware Sen. Tom Carper said he was concerned about whether parents can track down their kids.
According to an inside account of the president's retreat reported by the Washington Post, the president surprised aides - some of whom had gone out and aggressively defended the policy following their boss's lead - by asking them on Wednesday morning to prepare a draft executive order to end the controversial policy. "Jail is never an appropriate place for a child".
Amid an outcry in the United States over the policy, President Donald Trump has signed an executive order to keep families together. He did call on Congress to alleviate the plight of the separated children - but reiterated that his hands were tied.
A 2-year-old Honduran asylum seeker cries as her mother is searched and detained near the US-Mexico border on June 12, 2018 in McAllen, Texas.
"It's a bad situation", Welch, 43, said of the distraught children.
The typo is emblematic of the implementation of the Zero-Tolerance Policy.
'These are crippling loopholes which cause family separation, which we don't want'.
When asked specifically about the images of children being taken from their parents at immigration centers, Trump said that the images affected him.
The Associated Press reported on Tuesday night that "babies and other young children" are being sent to "tender age" shelters in Texas. Since its implementation, countless heartbreaking stories have emerged, including a mother who was deported while her son was kept in a USA facility and a father who committed suicide after being separated from his kids.