The Trump administration's "zero-tolerance" immigration policy had led to the separation of 2,342 children from their parents at the U.S. -Mexico border between May 5 and June 9.
Mr Trump has often chafed at this, which also leaves his party vulnerable to dissent by just one or two Republican senators.
News of the delay came at the same time the US House of Representatives failed by 193-231 to pass another, more conservative immigration bill, known as the Goodlatte bill after House Judiciary Chairman Bob Goodlatte, a conservative Republican from Virginia.
After spending the early part of the week insisting on the need for congressional immigration action, by Friday he had abandoned those efforts - tweeting that Republicans were "wasting their time" - and is girding for mid-term warfare. In a series of tweets, Trump said, "Dems are just playing games, have no intention of doing anything to solve this decades-old problem".
"Rather than encouraging people to vote for it, (Trump) gave them a reason not to vote for it by saying 'What's the point of having the vote if the Senate isn't going to pass it?'" he said.
The image, taken by award-winning photojournalist John Moore, became one of the iconic images used by the media to highlight coverage of the Trump's administration family separation immigration policy. Differences between conservative and moderate Republicans delayed a vote initially planned for yesterday.
Trump's latest Twitter crusade came after telling members, "I'm with you 100%" during a closed-door meeting Tuesday with House Republicans on immigration, according to a statement from White House principal deputy press secretary Raj Shah.
Key Republican lawmakers who have been involved in the negotiations said Friday that talks would continue through the weekend.
The Pentagon has begun drawing up plans to house as many as 20,000 migrants in United States military bases, and Immigration and Customs Enforcement is looking into creating 15,000 beds, but officials have given conflicting explanations on whether they would be for children or for families.
Trump's comments come amid an global outcry over the separation of migrant families at the southern border. And once they got 213 signatures on that document, Ryan scrambled to kill the effort by promising moderates a vote on similar legislation.
Zenen Jaimes Perez of the Texas Civil Rights Project said immigrant families are still awaiting details from the administration on how parents and children are to be reunited.
Administration officials on Wednesday refused to say what they would do with the migrant children in three weeks should they fail to get an exemption from a court or pass legislation through Congress.
Trump also said that if Republicans can win more seats in November, then they will be able to "pass the finest, fairest and most comprehensive" immigration bills.
Thursday, former Federal Bureau of Investigation director James Comey told an audience in London the family separations could be the president's most harmful misstep yet - and suggested Trump is trying to dodge the matter.
"You begin to see a border that is now highly marked not only by the wall, marked by the bridges, marked by the negative news, marked by the violence that as certainly changed dynamics", Moya said. If Democrats take control of the House, they are unlikely to approve that wall funding.
So, unless the White House backs off its "zero tolerance" policy (which it definitely won't), or the courts reverse themselves (which they nearly definitely won't), or Congress takes action, family separation will become USA policy again.
But as with the case of the travel ban, the reality of a vastly complicated bureaucratic system is colliding head-on with Trump's shoot-from-the-hip use of executive power. One outside White House adviser has called Miller a Nazi and Rep. Mike Coffman (R-Colo.) urged Trump to fire him on Thursday.
"We want safety in our country", he said.